Kerr-lens mode-locked operation of a Yb:KGW laser pumped by a multimode laser diode with the help of an additional Kerr medium is reported. With an enhanced Kerr lensing effect in the laser cavity operating far from the stability edge limit, the laser delivered 74 fs pulses with an average output power of 500 mW. In the high power regime of operation (>500 mW), the mode-locked laser output was accompanied by a continuous wave background radiation. Owing to the self-phase modulation effect, the laser demonstrated the generation of shorter pulses as compared to the case without an additional Kerr medium.