Eulerian and Hamiltonian Graphs · Superchallenge problem

Six cities $0,\ldots,5$ are joined by roads of every pair, with lengths (km) $01{:}6$, $02{:}8$, $03{:}10$, $04{:}4$, $05{:}9$, $12{:}5$, $13{:}7$, $14{:}11$, $15{:}3$, $23{:}4$, $24{:}6$, $25{:}8$, $34{:}5$, $35{:}7$, $45{:}6$. A salesperson starting and ending at city $0$ must visit every other city exactly once. What is the minimum possible total distance of the tour?