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DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization among its nucleotides. The formation of secondary structures makes the sequences chemically inactive towards synthesis and sequencing processes. In this letter, our goal is to tackle the problems due to the creation of secondary structures in DNA sequences along with constraints such as not having a large homopolymer run length. In this paper, we have presented families of DNA codes with secondary structures of stem length at most two and homopolymer run length at most four. By mapping the error correcting codes over $\Z_{11}$ to DNA nucleotides, we obtained DNA codes with rates $0.5765$ times the rate of corresponding code over $\Z_{11}$, which include some new secondary structure free and better-performing codes for DNA based data storage and DNA computing purposes., Comment: 10 pages, 2 figures