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In this work, we define three composite matrices derived from group rings. Weemploy these composite matrices to create generator matrices of the form [In |{\Omega}(v)], where In is the identity matrix and {\Omega}(v) is a compositematrix and search for binary self-dual codes with parameters [36, 18, 6 or 8].We next lift these codes over the ring R1 = F2 + uF2 to obtain codes whosebinary images are self-dual codes with parameters [72,36,12]. Many of thesecodes turn out to have weight enumerators with parameters that were not knownin the literature before. In particular, we find 30 new Type I binary self-dualcodes with parameters [72, 36, 12].

New Type I Binary [72, 36, 12] Self-Dual Codes from Composite Matrices and R1 Lifts