Expressing forms as a sum of pfaffians

Let A = (aij) be a symmetric non-negative integer 2k×2k matrix. A is homogeneous if aij + akl = ail + akj for any choice of the four indexes. Let A be a homogeneous matrix and let F be a general form in C[x1,...xn] with 2 deg(F) = trace(A). We look for the least integer, s(A), so that F = pfaff(M1) +...+ pfaff(Ms(A)), where the Mi = (Fi lm) are 2k × 2k skew-symmetric matrices of forms with degree matrix A. We consider this problem for n = 4 and we prove that s(A) ≤ k for all A.