  Given an augmentation for a Legendrian surface in a $1$-jet space, $\Lambda
\subset J^1(M)$, we explicitly construct an object, $\mathcal{F} \in
Sh_{\Lambda}$, of the (derived) category from arXiv:1402.0490 of constructible
sheaves on $M\times R$ with singular support determined by $\Lambda$. In the
construction, we introduce a simplicial Legendrian DGA (differential graded
algebra) for Legendrian submanifolds in $1$-jet spaces that, based on
arXiv:1608.02984 and arXiv:1608.03011, is equivalent to the Legendrian contact
homology DGA in the case of Legendrian surfaces. In addition, we extend the
approach of arXiv:1402.0490 for $1$-dimensional Legendrian knots to obtain a
combinatorial model for sheaves in $Sh_\Lambda$ in the $2$-dimensional case.
