We study a stochastic boundary value problem on (0,1)(d) of elliptic type in dimension d >= 4, driven by a coloured noise. An approximation scheme based on a suitable discretization of the Laplacian on a lattice of (0,1)(d) is presented; we also give the rate of convergence to the original stochastic partial differential equation in the L-p(Omega:L-2(D))-norm, for some values of p.