Eulerian and Hamiltonian Graphs · Superchallenge problem

Six warehouses $0,\ldots,5$ are linked by roads $14{:}5$, $04{:}3$, $35{:}4$, $23{:}6$, $12{:}2$, $01{:}7$, $25{:}3$, $05{:}8$, $34{:}5$ (km; no other roads exist, and every warehouse has exactly $3$ roads). A crew based at warehouse $0$ must clear every road and return to $0$, duplicating roads where cheapest. What is the minimum total distance?