Eulerian and Hamiltonian Graphs · Superchallenge problem

Six stations $0,\ldots,5$ sit in a loop with roads $01{:}5$, $12{:}6$, $23{:}4$, $34{:}5$, $45{:}9$, $50{:}7$ (going around), plus one direct shortcut road $03{:}25$ (no other roads exist). A crew based at $0$ must clear every road and return to $0$, duplicating roads where cheapest. What is the minimum total distance?