The category CM(B k,n ) of Cohen-Macaulay modules over a quotient B k,n of a preprojective algebra provides a categorification of the cluster algebra structure on the coordinate ring of the Grassmannian variety of k-dimensional subspaces in C n , [13]. Among the indecomposable modules in this category are the rank 1 modules which are in bijection with k-subsets of {1, 2,...,n}, and their explicit construction has been given by Jensen, King and Su. These are the building blocks of the category as any module in CM(B k,n ) can be filtered by them. In this paper we give an explicit construction of rank 2 modules. With this, we give all indecomposable rank 2 modules in the cases when k =3a n dk = 4. In particular, we cover the tame cases and go beyond them. We also characterise the modules among them which are uniquely determined by their filtrations. For k ≥ 4, we exhibit infinite families of non-isomorphic rank 2 modules having the same filtration.