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In this work, lifts of the binary self-dual codes to the ring family of $% R_{k}$ by using basic tools of linear algebra are described. By applying method to the extremal binary self-dual $[14,7,4]$ code in the specific case of $R_{2}$ , a family of self-dual codes over $R_{k}$ of length $14$ are constructed. As Gray images of these codes $[56,28,10]$ binary self-dual codes are obtained. Ten extremal binary self-dual $[58,29,10]$ codes with new weight enumerators are found as extensions of these codes. Magma package has been used to construct these codes.