The rectification of terahertz radiation in a periodically almost-depleted graphene structures with dual grating gate is studied. Plasmonic electron-hole ratchet based rectified current grows with decreasing the Fermi energy of charge carriers in the gated parts of graphene. It is shown that the charge carriers accumulated at boundaries of depleted parts of graphene enhance the magnitude and inhomogeneity of oscillating electric field of the plasmon, which leads to significant growth in the rectification efficiency. Interaction of plasmon modes in different gated parts of graphene can increase the rectification efficiency due to excitation of the hybrid plasmon modes.