Machine learning techniques are an active area of research for speech enhancement for hearing aids, with one particular focus on improving the intelligibility of a noisy speech signal. Recent work has shown that feature encodings from self-supervised speech representation models can effectively capture speech intelligibility. In this work, it is shown that the distance between self-supervised speech representations of clean and noisy speech correlates more strongly with human intelligibility ratings than other signal-based metrics. Experiments show that training a speech enhancement model using this distance as part of a loss function improves the performance over using an SNR-based loss function, demonstrated by an increase in HASPI, STOI, PESQ and SI-SNR scores. This method takes inference of a high parameter count model only at training time, meaning the speech enhancement model can remain smaller, as is required for hearing aids.