On the existence of extremal Type II codes over

Recently, there has been tremendous interest in self-dual codes over finite rings, specifically the rings Z2k. In this note, the first examples of extremal Type II codes over Z6 of length 32 are constructed. These give examples of extremal even unimodular lattices in dimension 32 by Construction A. A relationship between extremal Type II codes over Z6 and binary extremal Type II codes is also investigated.