Let $f(n)$ represent the number of ways one can fill a $3\times 3\times n$ tower with blocks of $2\times 1\times 1$.
You're allowed to rotate the blocks in any way you like; however, rotations, reflections etc of the tower itself are counted as distinct.

For example (with $q=100000007$):
$f(2)=229$,
$f(4)=117805$,
$f(10)modq=96149360$,
$f({10}^3)modq=24806056$,
$f({10}^6)modq=30808124$.

Find $f({10}^{10000})mod100000007$.