Accurate three-dimensional modelling of nonlinear pulse propagation within a gas-filled capillary is essential for understanding and improving the XUV yield in high harmonic generation. We introduce both a new model based on a multimode generalized nonlinear Schrödinger equation and a novel spatio-spectral measurement technique to which the model can be compared. The theory shows excellent agreement with the measured output spectrum and the spatio-spectral measurement reveals that the model correctly predicts higher order mode contributions to spectral broadening of the pulse. Fluorescence from the excited argon is used to verify the predicted ion distribution along the capillary.