  In this paper, we give a new upper bound on the minimum Euclidean weight of
Type II $\ZZ_{2k}$-codes and the concept of extremality for the Euclidean
weights when $k=3,4,5,6$. Together with the known result, we demonstrate that
there is an extremal Type II $\ZZ_{2k}$-code of length $8m$ $(m \le 8)$ when
$k=3,4,5,6$.
