  This work is a natural continuation of our previous work \cite{yz}. In this
paper, we give a complete classification of toric surface codes of dimension
less than or equal to 6, except a special pair, $C_{P_6^{(4)}}$ and
$C_{P_6^{(5)}}$ over $\mathbb{F}_8$. Also, we give an example, $C_{P_6^{(5)}}$
and $C_{P_6^{(6)}}$ over $\mathbb{F}_7$, to illustrate that two monomially
equivalent toric codes can be constructed from two lattice non-equivalent
polygons.
