With the development of information technology, huge amounts of data are produced at the same time. How to store data efficiently and at low cost has become an urgent problem. DNA is a high-density and persistent medium, making DNA storage a viable solution. In a DNA data storage system, the first consideration is how to encode the data effectively into code words. However, DNA strands are prone to non-specific hybridization during the hybridization reaction process and are prone to errors during synthesis and sequencing. In order to reduce the error rate, a thermodynamic minimum free energy (MFE) constraint is proposed and applied to the construction of coding sets for DNA storage. The Brownian multi-verse optimizer (BMVO) algorithm, based on the Multi-verse optimizer (MVO) algorithm, incorporates the idea of Brownian motion and Nelder-Mead method, and it is used to design a better DNA storage coding set. In addition, compared with previous works, the coding set has been increasing by 4%-50% in size and has better thermodynamic properties. With the improvement of the quality of the DNA coding set, the accuracy of reading and writing and the robustness of the DNA storage system are also enhanced.