Integrated sensing and communications (ISAC) is envisioned to be a key to advanced applications in future wireless networks. In this paper, we study the coded modulation designs for ISAC transmissions with short block lengths over correlated Rayleigh fading channels. In line with the short block length transmission, we consider the non-coherent communication detection and coherent radar sensing, where a neural network (NN)-assisted frame-wise constellation design is proposed. Specifically, we first derive the optimal communication and radar receivers. Then, we present some heuristic understandings of the code designs by considering special cases, based on which a conjecture on the optimal codes for the considered ISAC transmissions is developed. The constellation obtained from the proposed NN agrees with our conjecture and shows an important conclusion that the optimal codes of the considered problem may be a combination of the “on-off keying” and phase-shifted keying signalings. Our numerical results show that the proposed code exhibits promising communication and sensing performance simultaneously and outperforms the transmissions with a standard channel code and symbol-wise modulation.