Eulerian and Hamiltonian Graphs · Challenge problem

Four depots $0,1,2,3$ are joined by a road between every pair, with lengths $01{:}3$, $12{:}4$, $23{:}2$, $03{:}5$, $02{:}6$, $13{:}7$ (km). A crew based at depot $0$ must clear every road and return to $0$, duplicating roads where that is cheapest. What is the minimum total distance the crew must drive?