Polyelectrolyte gels with hydrophobic backbones exhibit complex phase behavior, such as the formation of various nanophases, that involves local segregation of the monomers. The formation of these inhomogeneous phases is mainly the consequence of the possible interactions on different length scales in the system, with electrostatic effects dominating over large length scales. In this work, we demonstrate the formation of nanophases in a model for a system of salt-free gel that incorporates entropic, elastic, electrostatic as well as solvent interactions. In particular, we analyze the system using both linear and nonlinear methods. Whereas the linear approximation properly identifies the region of instability against nanophase formation, it does not properly describe such nonlinear effects as the formation of very sharp interfaces between the nanosegregated regions. We further investigate the periodicity dependence as well as monomer and charge distributions for the gel as functions of different physical system parameters. Consequently, we determine that the range of solvent quality for nanophase segregation increases with increasing charge fraction and decreasing cross-link density.