Tardos proposed binary codes for fingerprinting with a code length of theoretically minimum order, and the related works mainly focused on the reduction of the code length were presented. We presented a concrete and systematic construction of the Tardos's fingerprinting code using a chaotic map. We also introduced a hierarchical structure to the codewords for the reduction of computational costs. However, there were room for improvement of the code-length of this structure. In this paper, we present the optimized hierarchical structure considering appropriate parameters under the assumption that the distribution of correlation scores follows Gaussian. In a computer simulation, we evaluate the collusion-resistance of optimized Tardos code and that of original non-layered Tardos code under theoretically equal condition.