In this paper we classify distance-regular graphs, including strongly regular graphs, ad-mitting a transitive action of the linear groups L(3; 2), L(3; 3), L(3; 4) and L(3; 5) for which the rank of the permutation representation is at most 15. We give details about constructed graphs. In addition, we construct self-orthogonal codes from distance-regular graphs obtained in this paper.