  A minimal code is a linear code where the only instance that a codeword has
its support contained in the support of another codeword is when the codewords
are scalar multiples of each other. Ashikhmin and Barg gave a sufficient
condition for a code to be minimal, which led to much interest in constructing
minimal codes that do not satisfy their condition. We consider a particular
family of codes $\mathcal C_f$ when $f$ is the indicator function of a set of
points, and prove a sufficient condition for $\mathcal C_f$ to be minimal and
not satisfy Ashikhmin and Barg's condition based on certain geometric
properties of the support of $f$. We give a lower bound on the size of a set of
points satisfying these geometric properties and show that the bound is tight.
