We investigate the potential of autoencoders (AEs) for building a joint communication and sensing (JCAS) system that enables communication with one user while detecting multiple radar targets and estimating their positions. Foremost, we develop a suitable encoding scheme for the training of the AE and for targeting a fixed false alarm rate of the target detection during training. We compare this encoding with the classification approach using one-hot encoding for radar target detection. Furthermore, we propose a new training method that complies with possible ambiguities in the target locations. We consider different options for training the detection of multiple targets. We can show that our proposed approach based on permuting and sorting can enhance the angle estimation performance so that single snapshot estimations with a low standard deviation become possible. We outperform an ESPRIT benchmark for small numbers of measurement samples.