In this paper, we constructed two nonzero homogeneous weight codes and three nonzero homogeneous weight codes (Two-weight and three-weight codes) over \({\mathbb {Z}}_{p^{m}}\) using projective Hjelmslev geometry. The Gray images of two-weight linear codes obtained over \({\mathbb {Z}}_{4}\) are optimal projective linear codes over \({\mathbb {F}}_{2}\) with respect to the Griesmer bound. Additionally, we looked into the minimum distance of the dual code using the columns of the generator matrices. Further, we discussed the applications of Gray images of constructed codes in secret sharing schemes and strongly regular graphs.
