  Extremal Type II $\mathbb{Z}_{8}$-codes are a class of self-dual
$\mathbb{Z}_{8}$-codes with Euclidean weights divisible by $16$ and the largest
possible minimum Euclidean weight for a given length. We introduce a doubling
method for constructing a Type II $\mathbb{Z}_{2k}$-code of length $n$ from a
known Type II $\mathbb{Z}_{2k}$-code of length $n$. Based on this method, we
develop an algorithm to construct new extremal Type II $\mathbb{Z}_8$-codes
starting from an extremal Type II $\mathbb{Z}_8$-code of type
$(\frac{n}{2},0,0)$ with an extremal $\mathbb{Z}_4$-residue code and length
$24, 32$ or $40$.
  We construct at least ten new extremal Type II $\mathbb{Z}_8$-codes of length
$32$ and type $(15,1,1)$. Extremal Type II $\mathbb{Z}_8$-codes of length $32$
of this type were not known before. Moreover, the binary residue codes of the
constructed extremal $\mathbb{Z}_8$-codes are optimal $[32,15]$ binary codes.
