Phase-modulated continuous-wave (PMCW) radar is an emerging technology in various civilian applications. Due to the high bandwidth of the PMCW signal, it needs high-speed analog-to-digital converters (ADCs). High-resolution ADCs supporting this high bandwidth are expensive, have a big size on the chip, and consume high power, which are significant challenges for radar. A solution to deal with the aforementioned challenges is to use low-resolution, or in the most extreme case, one-bit ADCs. In this article, we aim at designing the transmit code and the receive filter for the PMCW radar in the presence of one-bit ADC at the receiver side. To this end, we introduce the mean integrated sidelobe level metric, called MISL. MISL generalizes the well-known ISL metric for nonideal ADC usage at the receiver side and takes the effect of noise and target backscattering coefficient into account. For mathematical tractability, we employ the maximum likelihood estimation of the target backscattering coefficient. This leads to casting an optimization problem that does not need knowledge about noise and target characteristics. We utilize the cyclic optimization procedure to optimize the transmit code and the receive filter. The filter design subproblem admits a closed-form solution, whereas we obtain a solution to transmit code design subproblem via the coordinate descent framework. Numerical examples illustrate the superior performance of the proposed method compared to benchmarks that design sequences assuming ideal ADC at the receiver.