A Griesmer Bound for Codes over Finite Quasi-Frobenius Rings

In this article we give a Griesmer type bound for linear codes over finite quasi-Frobenius rings and consider codes over these rings meeting the bound. And we give a geometrical characterization of codes over finite chain rings meeting the bound, that is, one-to-one correspondence between the codes and minihyper in projective Hjelmslev spaces over these rings.