  Linear codes play a central role in coding theory and have applications in
several branches of mathematics. For error correction purposes the minimum
Hamming distance should be as large as possible. Linear codes related to
applications in Galois Geometry often require a certain divisibility of the
occurring weights. In this paper we present an algorithmic framework for the
classification of linear codes over finite fields with restricted sets of
weights. The underlying algorithms are based on lattice point enumeration and
integer linear programming. We present new enumeration and non-existence
results for projective two-weight codes, divisible codes, and additive
$\mathbb{F}_4$-codes.
