Let me quote the verse again from different sources.
avyakto ’kṣhara ityuktas tam āhuḥ paramāṁ gatim
yaṁ prāpya na
nivartante tad dhāma paramaṁ mama
This is the main quote from the Gita, as Krishna has uttered (rather as Ved Vyasa has written).
Now lets look at a few commentaries by different gurus. This will be long. So please have patience.
* RAMANUJA'S COMMENTARY (VISHISHTADVAITA)
Lord Krishna now reveals His superior conscious avyakta or unmanifest
which is different in principle and substance then the unconscious
avyakta or unmanifest of Brahma which is non-intelligent and operates
according to set parameters.
Lord Krishna's superior avyakta is characterised by eternality due to
its possession of ātma tattva or soul realisation. Thus it is also
characterised by jñāna or consciousness.
Avyakta is also known as indistinct because it beyond any perceptive
faculty of the mind or senses to cognise it as a perceivable reality.
The purport is that avyakta is a principle of self-consciousness and
as such is completely unique in its nature.
The word Sanātana meaning eternal because His superior avyakta is not
subject to combination and aggregation or resolution and
disintegration
and never disperses or dissipates when all the material elements of
earth, water, fire, air and ether in their rudimental forms and
derivative forms dissolve away, although His superior avyakta abides
within them.
This is why the Vedic scriptures call it avyakta or indistinct as well
as akṣara or indestructible.
Those steeped in the wisdom of the Vedic scriptures have declared that
this is the paramam gatim or supreme exalted goal to be achieved.
Lord Krishna previously mentioned akṣara in verse three of this
chapter and will later mention it again in chapters XII.III and
XV.XVI.
The superior state of avyakta is where ātma tattva or soul realisation
abounds and when once reached immediately precludes forever the
subjection to union with matter again as there is no more rebirth for
reincarnation has been terminated.
Lord Krishna specifies their destination with the words dhāma paramam
mama meaning His supreme personal abode of eternity, knowledge and
bliss where all things reciprocate fully with Him and is the abode of
the liberated beings.
The word dhāma also denotes luminosity as in the light of
consciousness which is the primary attribute of the ātma or soul.
Thus Lord Krishna is indicating His paramam dhāma as non-different
from the infinite consciousness of the ātma in contrast to the limited
state of consciousness one possesses,
who is oblivious to the ātma due to being deluded by the illusory
material energy known as māyā and cherishing the association of the
senses with sense objects.
The other avyakta where resides prakṛti or the material substratum
which contains all living entities and which is perishable is
controlled by Lord Krishna as well,
through His manifestation as the eternal ātma or soul within the
etheric heart of all created beings throughout all existence. This is
the abode of the non-liberated beings.
From the superior avyakta there is no return to samsāra the cycle of
birth and death.
* ADI SHANKARA'S COMMENTARY (ADVAITA)
He Himself who has been (uktah) mentioned; as (avyaktah) Unmanifest; the (aksarah) Immutable; (ahuh), they call; (tam), Him - that very unmanifest Reality which is termed as the Immutable; the Supreme Goal (paramam gatim). (Tat) That is the supreme abode (paramam dhama), i.e. the Supreme State; (mama), of Mine, of Vishnu; (yam prapya), reaching which Reality; (na nivartante) they do not return to the worldly state.
* MADHAVA'S COMMENTARY (DVAITA)
The avyakta, the unmanifest; and aksara, the indestructible is the resplendent Supreme Lord, Krishna Himself, upon whom attaining there is no more returning to samsara the perpetual cycle of birth and death. The Garuda Purana states: The avyakta is the Supreme Lord Himself. It shows the use of the word 'dhaama' or abode as also denoting the resplendent form of the Supreme Lord. Showing that the resplendent Supreme Lord’s form and abode are both indicated such are the confidential meanings understood by those of spiritual wisdom.
* SRI VISHVANATHA CHAKRAVARTHI THAKURA (ACHINTYA BHEDABHEDA)
The word avyakta of the previous verse is explained. That which is avyakta is without destruction: Narayana. As the sruti says, eko narayana asin na brahma na ca sankarah: one Narayana existed, and not Brahma or Siva. Attaining my eternal form (mama paramam dhama), they do not return.
The word aksara may also be interpreted as the impersonal brahman, in which case dhama paramam mama means “my form of light,” since dhama also means “light.”
Bottom line, what they are all trying to say is that the Supreme Destination is the Unmanifest form of the Lord which is technically Nirguna Brahman. Although Adi Shankara posits Nirguna Brahman as the ultimate reality, and the Supreme Reality, other Sampradayas don't accept this view. They believe in the Supremacy of Saguna, at the same time, not fully discounting this Unmanifest formless state of the Lord, which is (for the non-Advaita Vedantins) a state of perpetual bliss and jnana. For them the Saguna roop has control over their Nirguna roop. Whereas for Advaita it is both-ways, since there is no difference between the two. So the unanimous definition of this Param Dhama would be Satchidananda which is the purest state of existence that is not characterized by universal manifestation of forms (avyakta) and is immutable (aksarah), that since it is the first cause, it can never be muted. Rather all the other causes may be muted into this first cause hence its immutability is proved.
Let me support this with a verse from Katha Upanishad Chapter 2, Verse 22:
When the wise realize the Self
Formless in the midst of forms, changeless
In the midst of change, omnipresent
And supreme, they go beyond sorrow.
