Doppler division multiple access (DDMA) waveform shows great orthogonality for multiple-input multiple-output (MIMO) radar. However, it leads to a serious velocity ambiguous problem and hinders its application in automotive radar. In this work, a maximum unambiguous velocity extension approach is developed for DDMA MIMO radar by using a global ergodic optimization phase modulation during transmission. To be specific, we take the cumulative sum of the peak amplitude difference of global as the optimization cost function to obtain modulation codes. Furthermore, a matched filter phase demodulation carried out at the receiver to determine the results of angle measurement and velocity expansion. Finally, the simulation analysis and real-data experiments demonstrate our approach effectively improves velocity ambiguity resolving capabilities of DDMA waveform and suitable for massive MIMO array in nowadays automotive radar.