Self-dual Z4-codes and Hadamard matrices

In this note, we investigate Type I codes over Z4 constructed from Hadamard matrices. As an application, we construct a Type I Z4-code with minimum Euclidean weight 16 of length 40. This code is the first example of such a Type I Z4-code. This code also gives an example of a 40-dimensional extremal odd unimodular lattice with minimum norm 4.