Advancing ultrafast high-repetition-rate lasers to shortest pulse durations comprising only a few optical cycles while pushing their energy into the multi-millijoule regime opens a route toward terawatt-class peak powers at unprecedented average power. We explore this route via efficient post-compression of high-energy 1.2 ps pulses from an ytterbium InnoSlab laser to 9.6 fs duration using gas-filled multi-pass cells (MPCs) at a repetition rate of 1 kHz. Employing dual-stage compression with a second MPC stage supporting a close-to-octave-spanning bandwidth enabled by dispersion-matched dielectric mirrors, a record compression factor of 125 is reached at 70% overall efficiency, delivering 6.7 mJ pulses with a peak power of ∼0.3 TW. Moreover, we show that post-compression can improve the temporal contrast at multi-picosecond delay by at least one order of magnitude. Our results demonstrate efficient conversion of multi-millijoule picosecond lasers to high-peak-power few-cycle sources, prospectively opening up new parameter regimes for laser plasma physics, high energy physics, biomedicine, and attosecond science.