Eulerian and Hamiltonian Graphs · Hard problem

Five depots $0,1,2,3,4$ are linked by roads of these lengths (in km): $01{:}4$, $02{:}6$, $12{:}3$, $13{:}5$, $24{:}7$, $34{:}2$, $04{:}8$, $14{:}9$. A plow based at depot $0$ must clear every road and can retrace a road it has already cleared if that is cheaper than leaving a road uncleared. What is the minimum total distance (in km) the plow must drive to clear every road and return to depot $0$?