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For n\geq 2, there is a free field realization of the affine vertexsuperalgebra A associated to psl(n|n) at critical level inside thebc\beta\gamma system W of rank n^2. We show that the commutant C=Com(A,W) ispurely bosonic and is freely generated by n+1 fields. We identify the Zhualgebra of C with the ring of invariant differential operators on the space ofn\times n matrices under SL_n \times SL_n, and we classify the irreducible,admissible C-modules with finite dimensional graded pieces. For n\leq 4, C isisomorphic to the W_n^{(2)}-algebra at critical level, and we conjecture thatthis holds for all n.

A commutant realization of W^(2)_n at critical level