  We show how the theory of affine geometries over the ring ${\mathbb
Z}/\langle q - 1\rangle$ can be used to understand the properties of toric and
generalized toric codes over ${\mathbb F}_q$. The minimum distance of these
codes is strongly tied to the collections of lines in the finite geometry that
contain subsets of the exponent vectors of the monomials that are evaluated to
produce the standard generator matrix for the code. We argue that this
connection is, in fact, even more direct than the connection with the lattice
geometry of those exponent vectors considered as elements of ${\mathbb Z}^2$ or
${\mathbb R}^2$. This point of view should be useful both as a way to visualize
properties of these codes and as a guide to heuristic searches for good codes
constructed in this fashion. In particular, we will use these ideas to see a
reason why these constructions have been so successful over the field ${\mathbb
F}_8$, but less successful in other cases.
  This corrected version (posted on 3/6/2017) adds a necessary hypothesis in
Proposition 2.4. A counterexample to the previous version was pointed out to
the author by Melda G\"or\"ur and the author thanks her for bringing that to
his attention. Theorem 3.2 and Corollary 3.3 are also reformulated so they do
not refer to the new more restricted Proposition 2.4.
