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In this work, connected cubic planar bipartite graphs and related binaryself-dual codes are studied. Binary self-dual codes of length 16 are obtainedby face-vertex incidence matrices of these graphs. By considering their liftsto the ring R_2 new extremal binary self-dual codes of lengths 64 areconstructed as Gray images. More precisely, we construct 15 new codes of length64. Moreover, 10 new codes of length 66 were obtained by applying a building-upconstruction to the binary codes. Codes with these weight enumerators areconstructed for the first time in the literature. The results are tabulated.

New extremal binary self-dual codes of lengths 64 and 66 from bicubic planar graphs