This work presents an integrated pseudo-random binary sequence (PRBS) generator with programmable feedback designed in a 22nm fully-depleted silicon on insulator (FDSOI) technology. It shall be used as a modulation signal generator for ultra-wideband phase-modulated continuous-wave (PMCW) radars. Compared to standard linear-feedback shift registers (LFSRs) exhibiting fixed feedback, our circuit can generate different PRBSs. With this, we can distinguish between channels in MIMO systems but also reduce sidelobes resulting from spill-over and Doppler shifts. The LFSR is built of true single-phase-clock (TSPC) flip-flops, whose feedback is controlled by a high-speed digital circuit operating at one-fifth of the PRBS clock frequency. Measurements of the circuit show that the generator achieves a maximum bit rate of 27 to 31 Gb/s, depending on the number of activated feedback taps. While consuming 2.44mW, the proposed circuit is comparable to the current state of the art, offering better flexibility and radar performance.