Shortest Vector in a lattice on a Galois Field

Question

I am trying to solve the shortest vector problem, but on a galois field rather than the real numbers.

Say, for example, I am working in the field of integers modulo 7, $Z_7$. If I have the following lattice basis (where each column is a basis element), $$\begin{pmatrix}1 & 3 & 0\\\ 2 & 0 & -5\\\ 0&0&1\end{pmatrix}$$

I already have a working algorithm for enumerating every combination of these basis elements within a fundamental parallelepiped.

What differences should there be in my algorithm compared to if I was calculating the shortest vector over the real numbers?

I wonder:

1. Should the fundamental parallelepiped be different?
2. Should I be calculating the norm of every enumerated vector differently?