Decompositions and extremal type II codes over Z4

In previous work by Huffman and by Yorgov (1983), a decomposition theory of self-dual linear codes C over a finite field F_q was given when C has a permutation automorphism of prime order r relatively prime to q. We extend these results to linear codes over the Galois ring Z₄ and apply the theory to Z₄-codes of length 24. In particular we obtain 42 inequivalent [24,12] Z₄-codes of minimum Euclidean weight 16 which lead to 42 constructions of the Leech lattice