This letter presents an efficient algorithm for designing binary phase-coded sequences with low peak sidelobe level (PSL) for multiple-input multiple-output (MIMO) radar applications. The algorithm features a log-sum-exp function (LSEF)-based fitness function and a vectorized recursive computation method, substantially reducing computational complexity compared to conventional approaches. A two-stage search strategy effectively balances between local exploitation and global exploration. Numerical results demonstrate that the proposed algorithm achieves comparable PSL performance to state-of-the-art algorithms with enhanced computational efficiency in monostatic cases, while exhibiting superior PSL performance in MIMO scenarios.