When an intense, few-cycle light pulse impinges on a dielectric or semiconductor material, the electric field will interact nonlinearly with the solid, driving a coherent current. An asymmetry of the ultrashort, carrier-envelope-phase-stable waveform results in a net transfer of charge, which can be measured by macroscopic electric contact leads. This effect has been pioneered with extremely short, single-cycle laser pulses at low repetition rate, thus limiting the applicability of its potential for ultrafast electronics. We investigate lightwave-driven currents in gallium nitride using few-cycle laser pulses of nearly twice the duration and at a repetition rate two orders of magnitude higher than in previous work. We successfully simulate our experimental data with a theoretical model based on interfering multiphoton transitions, using the exact laser pulse shape retrieved from dispersion-scan measurements. Substantially increasing the repetition rate and relaxing the constraint on the pulse duration marks an important step forward towards applications of lightwave-driven electronics.