  A bidimensional bifix (in short bibifix) of a square matrix T is a square
submatrix of T which occurs in the top-left and bottom-right corners of T. This
allows us to extend the definition of bifix-free words and cross-bifix-free set
of words to bidimensional structures. In this paper we exhaustively generate
all the bibifix-free square matrices and we construct a particular
non-expandable cross-bibifix-free set of square matrices. Moreover, we provide
a Gray code for listing this set.
