The $2$-closure of a $\frac32$-transitive group in polynomial time

Let $G$ be a permutation group on a finite set $\Omega$. The $k$-closure $G^{(k)}$ of $G$ is the largest subgroup of the symmetric group $\mathrm{Sym}\,(\Omega)$ having the same orbits with $G$ on the $k$th Cartesian power $\Omega^k$ of $\Omega$. The group $G$ is called $\frac32$-transitive, if $G$ is transitive and the orbits of a point stabilizer $G_a$ on $\Omega\{a\}$ are of the same size greater than $1$. We prove that the $2$-closure $G^{(2)}$ of a $\frac32$-transitive permutation group $G$ can be found in polynomial time in size of $\Omega$. Moreover, if the group $G$ is not $2$-transitive, then for every positive integer $k$ its $k$-closure can be found within the same time. Applying the result, we prove the existence of a polynomial-time algorithm for solving the isomorphism problem for schurian $\frac32$-homogeneous coherent configurations, that is coherent configurations naturally associated with $\frac32$-transitive groups.