We report on the enhancement of high harmonic generation (HHG) yield in a metasurface consisting of amorphous silicon disks in a periodic array on an insulator substrate. The structure was designed and optimized using the finite-difference time-domain method for the maximum enhancement, which reaches the factor of 20-times compared to the unstructred surface. The local field is enhanced by a broadband magnetic resonance mode allowing to use ultrashort laser pulses with Fourier transform limit down to 40 fs. Due to the anisotropic structure of the metasurface, both the local-field enhancement and the HHG yield show strong polarization anisotropy.