Eddy current induced field perturbations can cause artifacts in diffusion weighted imaging (DWI). Such perturbations may be calculated and corrected for by the gradient system transfer function (GSTF), provided the gradient system behaves linear and time-invariant. We discovered that the linearity assumption can be violated by gradients with high zeroth order moments. We therefore propose a modified measurement scheme for the GSTF including higher gradient moments to better approximate their behavior. Our approach substantially reduces errors in the predicted gradient time courses. We may thus enable the application of GSTF-based correction methods to DWI in the future.