Eulerian and Hamiltonian Graphs · Superchallenge problem

The Möbius ladder $M_6$ has $12$ vertices on a $12$-cycle: $0,1,\ldots,11$ where $i$ connects to $i+1 \pmod{12}$. Additionally, it has six rungs $i$ to $i+6 \pmod{12}$ for $i=0,\ldots,5$. A delivery truck must traverse every road at least once, starting and ending at the same depot. What is the minimum total number of roads (counting multiplicity) the truck must travel?