  We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We
find Singleton bounds with respect to this weight and define MLDS and MLDR
codes accordingly. We also consider the kernels of these codes and the notion
of independence of vectors in this space. We investigate the linearity and
duality of the Gray images of codes over $\mathbb{Z}_{p^s}$.
