Supercompilers look for the best execution order of the statement instances in the most compute intensive kernels. It has been extensively shown that the polyhedral model provides convenient abstractions to find and perform the useful program transformations. Nevertheless, the current polyhedral code generation algorithms lack for flexibility by adressing mainly unimodular or at least invertible transformation functions. Moreover, their complexity is challenging for large problems (with many statements). In this paper, we discuss a general transformation framework able to deal with non-unimodular, non-invertible functions. A completed and improved version of one of the best algorithms known so far is presented to actually perform the code generation. Experimental evidence proves the ability of our framework to handle real-life problems.