We address the problem of radar phase‐coded waveform design for extended target recognition in the presence of colored Gaussian disturbance. Phase‐coded waveforms are selected since they can fully exploit the transmit power with sufficient variability. An important constraint, target detection performance, is considered to meet the practical requirements. The waveform is designed to achieve maximum recognition performance under a control on the achievable signal‐to‐noise ratio (SNR) of every possible target hypothesis. We formulate the code design in terms of a nonconvex, NP‐hard quadratic optimization problem in the cases of both continuous and discrete phases. Techniques based on semidefinite relaxation (SDR) and randomization are proposed to approximate the optimal solutions. Simulation results show that the recognition performance and the detection requirements are well balanced and accurate approximations are achieved.