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