Eulerian and Hamiltonian Graphs · Challenge problem

Five cities $0,1,2,3,4$ have direct roads of lengths $01{:}4$, $02{:}9$, $03{:}7$, $04{:}3$, $12{:}5$, $13{:}6$, $14{:}8$, $23{:}2$, $24{:}6$, $34{:}5$ (every pair is linked). A salesperson starting at city $0$ must visit every other city exactly once and return to city $0$. What is the minimum possible total distance?