  Multilevel lattice codes, such as those associated to Constructions $C$,
$\overline{D}$, D and D', have relevant applications in communications. In this
paper, we investigate some properties of lattices obtained via Constructions D
and D' from $q$-ary linear codes. Connections with Construction A, generator
matrices, expressions and bounds for the lattice volume and minimum distances
are derived. Extensions of previous results regarding construction and decoding
of binary and $p$-ary linear codes ($p$ prime) are also presented.
