New extremal Type II Z4-codes of length 32 obtained from Hadamard matrices

For every Hadamard design with parameters 2-(n - 1, n/2 - 1, n/4 - 1) having a skew-symmetric incidence matrix we give a construction of 54 Hadamard designs with parameters 2-(4n - 1, 2n - 1, n - 1). Moreover, for the case n = 8 we construct doubly-even self-orthogonal binary linear codes from the corresponding Hadamard matrices of order 32. From these binary codes we construct five new extremal Type II Z(4)-codes of length 32. The constructed codes are the first examples of extremal Type II Z(4)-codes of length 32 and type 4(k1)2(k2), k(1) is an element of {7, 8, 9, 10}, whose residue codes have minimum weight 8. Further, correcting the results from the literature we construct 5147 extremal Type II Z(4)-codes of length 32 and type 4(14)2(4).