We construct planar polynomial differential systems of even (respectively odd) degree n > 3, of linear form plus a nonlinear homogeneous part of degree n having a weak focus of order n2 - 1, respectively (n2 - 1)/2, at the origin. As far as we know this provides the highest order known until now for a weak focus of a polynomial differential system of arbitrary degree n. Copyright © 2012 Rocky Mountain Mathematics Consortium.