  A Type IV-II Z4-code is a self-dual code over Z4 with the property that all
Euclidean weights are divisible by eight and all codewords have even Hamming
weight. In this paper we use generalized bent functions for a construction of
self-orthogonal codes over Z4 of length $2^m$, for $m$ odd, $m \geq 3$, and
prove that for $m \geq 5$ those codes can be extended to Type IV-II Z4-codes.
From that family of Type IV-II Z4-codes, we obtain a family of self-dual Type
II binary codes by using Gray map. We also consider the weight distributions of
the obtained codes and the structure of the supports of the minimum weight
codewords.
