  We construct distance-regular graphs, including strongly regular graphs,
admitting a transitive action of the Chevalley groups $G_2(4)$ and $G_2(5)$,
the orthogonal group $O(7,3)$ and the Tits group $T=$$^2F_4(2)'$. Most of the
constructed graphs have more than 1000 vertices, and the number of vertices
goes up to 28431. Some of the obtained graphs are new.
