Convolutional Self-Doubly Orthogonal Codes (CSO²C) have been introduced in 1998 by Haccoun et al. as a novel class of convolutional codes which can be decoded using an iterative threshold decoding algorithm that does not require interleavers. However, these codes need to satisfy some orthogonal properties. Moreover, the memory length of the code is a key issue for their overall latency. Unfortunately, the design of CSO²C codes with minimum span corresponds to a highly combinatorial problem and only heuristics have been proposed up to now. We here investigate different mathematical programming formulations for the optimum design of CSO²C codes, or, at least, for deriving a lower bound on their optimum span in order to evaluate the quality of the heuristic solutions. It therefore leads to an assessment on the length of the best known CSO²C codes.