Channel charting is an unsupervised learning task whose objective is to encode channels so that the obtained representation reflects the relative spatial locations of the corresponding users. It has many potential applications, ranging from user scheduling to proactive handover. In this paper, a channel charting method is proposed, based on a distance measure specifically designed to reduce the effect of small scale fading, which is an irrelevant phenomenon with respect to the channel charting task. A nonlinear dimensionality reduction technique aimed at preserving local distances (Isomap) is then applied to actually get the channel representation. The approach is empirically validated on realistic synthetic \new{multipath} MIMO channels, achieving better results than previously proposed approaches, at a lower cost.