  We consider the Dirichlet problem for a class of quasilinear elliptic systems
in domain with irregular boundary. The principal part satisfies componentwise
coercivity condition and the nonlinear terms are Carath\'eodory maps having
Morrey regularity in $x$ and verifying controlled growth conditions with
respect to the other variables. We have obtained boundedness of the weak
solution to the problem that permits to apply an iteration procedure in order
to find optimal Morrey regularity of its gradient.
