The diagnosis of multiple sclerosis (MS) is usually based on clinical symptoms and signs of damage to the central nervous system, which is assessed using magnetic resonance imaging. The correct interpretation of these data requires excellent clinical expertise and experience. Deep neural networks aim to assist clinicians in identifying MS using imaging data. However, before such networks can be integrated into clinical workflow, it is crucial to understand their classification strategy. In this study, we propose to use a convolutional neural network to identify MS patients in combination with attribution algorithms to investigate the classification decisions. The network was trained using images acquired with susceptibility-weighted imaging (SWI), which is known to be sensitive to the presence of paramagnetic iron components and is routinely applied in imaging protocols for MS patients. Different attribution algorithms were used to the trained network resulting in heatmaps visualizing the contribution of each input voxel to the classification decision. Based on the quantitative image perturbation method, we selected DeepLIFT heatmaps for further investigation. Single-subject analysis revealed veins and adjacent voxels as signs for MS, while the population-based study revealed relevant brain areas common to most subjects in a class. This pattern was found to be stable across different echo times and also for a multi-echo trained network. Intensity analysis of the relevant voxels revealed a group difference, which was found to be primarily based on the T1w magnitude images, which are part of the SWI calculation. This difference was not observed in the phase mask data.