The shape instability of magnetic domain walls under current is investigated in a ferromagnetic (Ga,Mn)(As,P) film with perpendicular anisotropy. Domain wall motion is driven by the spin transfer torque mechanism. A current density gradient is found either to stabilize domains with walls perpendicular to current lines or to produce finger-like patterns, depending on the domain wall motion direction. The instability mechanism is shown to result from the non-adiabatic contribution of the spin transfer torque mechanism. ; Comment: 5 pages, 3 figures + supplementary materials