Can i use Babai algorithm in q-ary lattice
No, you can't.

Babai's Nearest Plane Algorithm is supposed to receive a basis of the lattice, and $\mathbf{A}$ is not the basis of the modular lattice that it spans. If you give Babai's algorithm the matrix ${\bf A}$, it will work over the lattice $ \mathcal{L}({\bf A}) := \{ {\bf A}{\bf x} : {\bf x} \in \mathbb{Z}^n  \}$ instead of $\mathcal{L}_q({\bf A}) $. Therefore, it will probably output wrong answers.

For instance, if you take a vector $\mathbf{t} = (q, q, ..., q)$, then $\mathbf{t} \in \mathcal{L}_q({\bf A})$, therefore, Babai's algorithm must output $\mathbf{t}$ itself. But it is likely that $\mathbf{t} \not \in \mathcal{L}({\bf A})$, so, Babai's algorithm will output some vector different from ${\bf t}$.