  Let C be a binary self-dual code with an automorphism g of order 2p, where p
is an odd prime, such that g^p is a fixed point free involution. If C is
extremal of length a multiple of 24 all the involutions are fixed point free,
except the Golay Code and eventually putative codes of length 120. Connecting
module theoretical properties of a self-dual code C with coding theoretical
ones of the subcode C(g^p) which consists of the set of fixed points of g^p, we
prove that C is a projective F_2<g>-module if and only if a natural projection
of C(g^p) is a self-dual code. We then discuss easy to handle criteria to
decide if C is projective or not. As an application we consider in the last
part extremal self-dual codes of length 120, proving that their automorphism
group does not contain elements of order 38 and 58.
