  We consider a model initial- and Dirichlet boundary- value problem for a
linearized Cahn-Hilliard-Cook equation, in one space dimension, forced by the
space derivative of a space-time white noise. First, we introduce a canvas
problem the solution to which is a regular approximation of the mild solution
to the problem and depends on a finite number of random variables. Then,
fully-discrete approximations of the solution to the canvas problem are
constructed using, for discretization in space, a Galerkin finite element
method based on $H^2$ piecewise polynomials, and, for time-stepping, an
implicit/explicit method. Finally, we derive a strong a priori estimate of the
error approximating the mild solution to the problem by the canvas problem
solution, and of the numerical approximation error of the solution to the
canvas problem.
