Weights modulo pe of linear codes over rings

In this paper we look at linear codes over the Galois ring GR(p(l),m) with the homogeneous weight and we prove that the number of codewords with homogeneous weights in a particular residue class modulo p(e) are divisible by high powers of p. We also state a result for a more generalized weight on linear codes over Galois rings. We obtain similar results for the Lee weights of linear codes over F-2m + uF(2m) and we prove that the results we obtain are best possible. The results that we obtain are an improvement to Wilson's results in [Wilson RM (2003) In: Proceedings of international workshop on Cambridge linear algebra and graph coloring].