We consider a joint communications and sensing (JCAS) system operating at mm-waves that jointly maximizes both functionalities' performance. Firstly, we propose a novel multibeam algorithm for JCAS systems, providing multiple simultaneous transmit beams to support efficient communications, while a separate beam simultaneously senses the environment. The proposed algorithm simultaneously implements interference control to mitigate possible interference stemming from the communication beam, while effective self-interference cancellation suppresses the direct transmitter-receiver leakage. Secondly, the joint waveform is optimized through the minimization of delay estimation error, which also ascertains that the performance of the communication system is at an acceptable level. The results showcase the trade-off between the performance of the communication system and the sensing functionality, but also demonstrate the high performance of the proposed JCAS system.