Hitting Time from Leaf to Root on a Complete Ternary Tree

Consider the complete ternary tree of depth $2$: a root vertex $r$ with $3$ children, each of which has $3$ children (leaves), giving $13$ vertices total. A simple random walk moves at each step to a uniformly random neighbor. Starting from a leaf vertex, what is the expected number of steps to reach the root $r$ for the first time?