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This graph has m=90 edges so counting from 0 to 2^m will not finish in your lifetime. Exhaustive search is only feasible up to 30 edges.

Your specific problem (finding a 4-connected planar spanning subgraph) can be solved in a few seconds by guessing subgraphs using plantri:

from sage.graphs.generic_graph_pyx import SubgraphSearch

G = Graph("S~KzzNbo]@oB?F?^_}W]FB@{[E[o[^oWK")
for H in graphs.plantri_gen(f"{G.order()} -pc4"):
    for _ in SubgraphSearch(G, H):
        return H