  The MacWilliams Extension Theorem states that each linear Hamming isometry of
a linear code extends to a monomial map. In this paper an analogue of the
extension theorem for linear codes over a module alphabet is observed. A
geometric approach to the extendability of isometries is described. For a
matrix module alphabet we found the minimum length of a code for which an
unextendable Hamming isometry exists. We also proved an extension theorem for
MDS codes over a module alphabet.
