A group of $2\times 2$-matrices which is isomorphic to $\left(\mathcal{O}/24\mathcal{O}\right)^{\times}$ where $\mathcal{O}=\mathbb{Z}[\sqrt{-3}]$ Is there a subgroup $G\leq\mathrm{Gl}_2(\mathbb{Z}_n)$ such that $G\cong\left(\mathcal{O}/n\mathcal{O}\right)^{\times}$ where $\mathcal{O}=\mathbb{Z}[\sqrt{-3}]$ and for a ring $R$, $R^{\times}$ denotes the group of units of $R$?
If yes (which seems to be the case, intuitionally), how does one construct it?
Some context: I am particularly looking for a group of $2\times 2$-matrices which is isomorphic to $\left(\mathcal{O}/24\mathcal{O}\right)^{\times}$.
I would very much appreciate it if somebody could point it out to me.

$GL_2(\Bbb{Z}/n\Bbb{Z})=Aut((\Bbb{Z}/n\Bbb{Z})^2)$. Obviously $\Bbb{Z}[\sqrt{-3}]/(n)$ is isomorphic to $(\Bbb{Z}/n\Bbb{Z})^2$ as a group and choosing such an isomorphism multiplication by elements of $\Bbb{Z}[\sqrt{-3}]/(n)^\times$ give automorphisms $\in Aut((\Bbb{Z}/n\Bbb{Z})^2)$.
