We study a problem related to Kontsevich's homological mirror symmetry conjecture for the case of a generic curved with bi-degree (2,2) in a product of projective lines P-1 x P-1. We calculate two differenent monodromy representations of period integrals for the affine variety x((2,2)) obtained by the dual polyhedron mirror variety construction from y. The first method that gives a full representation of the fundamental group of the complement to singular loci relies on the generalised Picard-Lefschetz theorem. The second method uses the analytic continuation of the Mellin-Barnes integrals that gives us a proper subgroup of the monodromy group. It turns out both representations admit a Hermitian quadratic invariant form that is given by a Gram matrix of a split generator of the derived category of coherent sheaves on on Id with respect to the Euler form.