Codebook design for code-domain non-orthogonal multiple access (CD-NOMA) can be considered as a multi-user multi-dimensional modulation (MU-MDM) design. However, the sheer complexity of assigning multiple bits from multiple users to signal points in multi-dimension signal space, while minimizing bit-error rate (BER), had limited its practicality. Inspired by its ability to approximate complex optimization methods, this paper proposes an autoencoder (AE)-based MU-MDM design. In this regard, a novel loss function is proposed which simultaneously considers Euclidean distance between signal points and Hamming distance between bits assigned to neighboring signal points. Extensive simulation results show that the proposed AE-based design has 1.5dB gain over the state-of-the-art MU-MDM designs in both sparse and dense codebook setting. Furthermore, it is shown that the low complexity of deep learning (DL)-based receiver allows for employing dense CD-NOMA as compared to the conventional receivers which require codebooks to be sparse to reduce its implementation complexity.