Physical-layer key generation (PLKG) has emerged as a promising technique to secure next-generation wireless networks by exploiting the inherent properties of the wireless channel. However, PLKG faces fundamental challenges in the millimeter wave (mmWave) regime due to channel sparsity, higher phase noise, and higher path loss, which undermine both the randomness and reciprocity required for secure key generation. In this paper, we present mmKey, a novel PLKG framework that capitalizes on the availability of multiple antennas at mmWave wireless nodes to inject randomness into an otherwise quasi-static wireless channel. Different from prior works that sacrifice either the secrecy of the key generation or the robustness, mmKey balances these two requirements. In particular, mmKey leverages a genetic algorithm to gradually evolve the initial weight vector population toward configurations that suppress the LOS component while taking into account the channel conditions, specifically, the sparsity and the signal-to-noise ratio (SNR). Extensive simulations show that mmKey improves the secrecy gap by an average of 39.4% over random beamforming and 34.0% over null beamforming, outperforming conventional schemes.