On automorphisms of a distance-regular graph with intersection of arrays {39, 30, 4; 1, 5, 36}

J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue $\leq t$ for a given positive integer t. This problem is reduced to the description of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with non-principal eigenvalue t for t =1,2,... Let $\Gamma$ be a distance regular graph of diameter $3$ with eigenvalues $\theta_0>\theta_1>\theta_2>\theta_3$. If $\theta_2= -1$, then by Proposition 4.2.17 from the book "Distance-Regular Graphs" (Brouwer A. E., Cohen A. M., Neumaier A.) the graph $\Gamma_3$ is strongly regular and $\Gamma$ is an antipodal graph if and only if $\Gamma_3$ is a coclique. Let $\Gamma$ be a distance-regular graph and the graphs $\Gamma_2$, $\Gamma_3$ are strongly regular. If k