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We find new extremal [76,38,14] and [78,39,14] binary self-dual codes. The code of length 76 is the first known self-dual code with these parameters. It is shadow extremal and the shortest known self-dual code with minimal distance 14. It has an automorphism of order 19 without fixed coordinates. The code of length 78 has a new weight enumerator and an automorphism of order 19 with two fixed coordinates.