Finite group rings carry a natural involution that defines a form ring structure. We investigate the associated Clifford-Weil groups for the indecomposable representations of the groups of order $2,3$ and the symmetric group ${\mathrm{Sym}}_3$ over the fields with $2$ and $3$ elements as well as suitable symmetrizations. An analogue of Kneser’s neighboring method is introduced, to classify all self-dual codes in a given representation.