Phase-Coded frequency-modulated continuous-wave (PC-FMCW) radar is an emerging radar system with its unique features such as enabling joint sensing and communication or advanced interference mitigation. Even though radars with phase coding capabilities are available in the automotive radar market today, there are some challenges in phase coded radar applications. With this paper we demonstrate multiple bit coding per single transmit chirp waveform in a FMCW automotive radar system for the first time. We concentrate on the sensing aspect of PC-FMCW radar and point out the challenges due to instantaneous phase change. To overcome these issues and improve sensing performance, this paper proposes a smart filtering method which consists of rejection filtering and signal recovery steps.