Uniqueness and nonexistence of some graphs related toM22

There is a unique distance regular graph with intersection array i (7, 6, 4, 4; 1, 1, 1, 6); it has 330 vertices, and its automorphism groupM22.2 acts distance transitively. It does not have an antipodal 2-cover, but it has a unique antipodal 3-cover, and this latter graph has automorphism group 3.M22.2 acting distance transitively. As a side result we show uniqueness of the strongly regular graph with parameters (v, k, λ, μ) = (231, 30, 9, 3) under the assumption that it is a gamma space with lines of size 3.