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The theory of linear codes over finite fields has been extended by A. Nechaev to codes over quasi-Frobenius modules over commutative rings, and by J. Wood to codes over (not necessarily commutative) finite Frobenius rings. In the present paper, we subsume these results by studying linear codes over quasi-Frobenius and Frobenius modules over any finite ring. Using the character module of the ring as alphabet, we show that fundamental results like MacWilliams' theorems on weight enumerators and code isometry can be obtained in this general setting.