The emission of high-order harmonics in the extreme ultraviolet range from the interaction of a short, intense laser pulse with a grating target is investigated experimentally. When resonantly exciting a surface plasmon, both the intensity and the highest order observed for the harmonic emission along the grating surface increase with respect to a flat target. Harmonics are obtained when a suitable density gradient is preformed at the target surface, demonstrating the possibility to manipulate the grating profile on a nanometric scale without preventing the surface plasmon excitation. In support of this, the harmonic emission is spatiotemporally correlated to the acceleration of multi-MeV electron bunches along the grating surface. Particle-in-cell simulations reproduce the experimental results and give insight on the mechanism of high harmonic generation in the presence of surface plasmons.