In massive machine-type communications (mMTC), grant-free access is a key enabler for a massive number of users to be connected to a base station with low signaling overhead and low latency. In this paper, a two-stage genetic algorithm (GA) is proposed to design a new set of user-specific, non-orthogonal, unimodular sequences for uplink grant-free access. The first-stage GA is to find a subsampling index set for a partial unitary matrix that can be approximated to an equiangular tight frame. Then in the second-stage GA, we try to find a sequence to be masked to each column of the partial unitary matrix, in order to reduce the peak-to-average power ratio of the resulting columns for multicarrier transmission. Finally, the masked columns of the matrix are proposed as new non-orthogonal sequences for uplink grant-free access. Simulation results demonstrate that the non-orthogonal sequences designed by our two-stage GA exhibit excellent performance for compressed sensing based joint activity detection and channel estimation in uplink grant-free access. Compared to algebraic design, this GA-based design can present a set of good non-orthogonal sequences of arbitrary length, which provides more flexibility for uplink grant-free access in mMTC.