  This paper examines the $w$-weight enumerators of weights $w$ with maximal
symmetry over finite chain rings and matrix rings over finite fields. In many
cases, including the homogeneous weight, the MacWilliams identities for
$w$-weight enumerators fail because there exist two linear codes with the same
$w$-weight enumerator whose dual codes have different $w$-weight enumerators.
