  A finite set of distinct vectors $\mathcal{X}$ in the $d$-dimensional
Euclidean space $\mathbb{R}^d$ is called a $2$-distance set, if the set of
mutual distances between distinct elements of $\mathcal{X}$ has cardinality
exactly $2$. In this note we classify the $2$-distance sets in $\mathbb{R}^4$
up to isometry with computer-aided methods.
