Eulerian and Hamiltonian Graphs · Hard problem

Six stops $0,1,2,3,4,5$ are linked by weighted roads: $01{:}4$, $02{:}7$, $12{:}3$, $13{:}6$, $23{:}2$, $24{:}5$, $34{:}4$, $35{:}8$, $45{:}3$, $14{:}9$, $25{:}10$ (no other roads exist). A courier must start at stop $0$, visit every other stop exactly once, and finish at stop $5$. What is the minimum possible total distance?