This work presents an extension of the Construction $π_A$ lattices proposed in \cite{huang2017construction}, to Hurwitz quaternion integers. This construction is provided by using an isomorphism from a version of the Chinese remainder theorem applied to maximal orders in contrast to natural orders in prior works. Exploiting this map, we analyze the performance of the resulting multilevel lattice codes, highlight via computer simulations their notably reduced computational complexity provided by the multistage decoding. Moreover it is shown that this construction effectively attain the Poltyrev-limit.