On codes with distances $d$ and $n$

We enumerate all $q$-ary additive (in particular, linear) block codes of length $n$ and cardinality $N\geqslant q^2$ with exactly two distances: $d$ and $n$. For arbitrary codes of length $n$ with distances $d$ and $n$, we obtain upper bounds on the cardinality via linear programming and using relationships to $2$-distance sets on a Euclidean sphere.