We generalize the Plotkin-type Lee distance bound for linear codes over Z4to several new and stronger bounds. We apply these bounds to determine all possible integersnsuch that Plotkin-optimal linear codes over Z4of lengthnand type 4k12k2exist for any given non-negative integersk1andk2. We furthermore provide construction methods for Plotkin-optimal linear codes over Z4for each possible length mentioned above. Our results are in large part established by considering column multiplicities of generator matrices.

We show that linear codes over Zpmsatisfy two extended versions of Wei’s Duality Theorem with respect to generalized Hamming weights (GHW) and a natural extension of GHW. Our results use a different approach to obtaining Wei-type duality theorems by extending the well-known relation between GHW and column multiplicities for linear codes over finite fields. We also present several new bounds for the minimum Lee distance of linear codes over Zpmthat arise from the Singleton-type bound with respect to GHW. Our bounds generalize and improve several existing minimum Lee distance bounds.