By combining a lattice subgroup diagram of Z_m with a weighted poset metric, we introduce a new weighted coordinates poset metric for codes over Z_m , called LS-poset metric. When I is an ideal in a poset, the concept of I-perfect codes with LS-poset metric is investigated. We obtain a Singleton bound for codes with LS-poset metric and define MDS codes. When the poset in poset metric is a chain, we provide sufficient conditions for a code with LS-poset metric to be r-perfect for some r ∈ N .