It is a central problem in the research of coding to study the existence, structure and construction of the certain optimal property codes. In order to construct the quantum error-correcting codes, people have begun to study the self-orthogonal code that has the special self-dual distance. In this paper, two classes of sub-codes, which have optimal dual distance or intended optimal dual distance, of the binary non-decomposable self-dual codes of length n between 12 and 20, such as B12, D14, E16, F16, H18, I18, J20, K20, L20, M20 and S20, and the corresponding S-chain construction are studied. Based on the generator matrices of the self-dual codes, optimal sub-codes of dual distance 2, 3 and 4 of these self-dual codes are constructed by using a combinational method. Then code chains of these optimal sub-codes and their dual codes are discussed. Consequently, S-chains are constructed from these sub-codes with optimal dual distance or intended optimal dual distance. Finally, some very good quantum error-correcting codes are constructed from the S-chains obtained. These quantum codes are the ones that the distance reaches the maximum when their n and k are given.