Monomials of orders 7 and 11 cannot be in the group of a (24, 12, 10) self-dual quaternary code

It is an interesting open question whether a self-dual quaternary (24,12,10) code C exists. It was shown by Conway and Pless that the only primes which can be orders of permutations in the group of C are 11, 7, and 3. In this correspondence we eliminate 11 and 7 not only as permutations but also as orders of monomials in the group of C . This is done by reducing the problems to the consideration of several codes and finding low weight vectors in these codes.