Recent advances in distant-talking ASR research have confirmed that speech enhancement is an essential technique for improving the ASR performance, especially in the multichannel scenario. However, speech enhancement inevitably distorts speech signals, which can cause significant degradation when enhanced signals are used as training data. Thus, distant-talking ASR systems often resort to using the original noisy signals as training data and the enhanced signals only at test time, and give up on taking advantage of enhancement techniques in the training stage. This paper proposes to make use of enhanced features in the student-teacher learning paradigm. The enhanced features are used as input to a teacher network to obtain soft targets, while a student network tries to mimic the teacher network's outputs using the original noisy features as input, so that speech enhancement is implicitly performed within the student network. Compared with conventional student-teacher learning, which uses a better network as teacher, the proposed selfsupervised method uses better (enhanced) inputs to a teacher. This setup matches the above scenario of making use of enhanced features in network training. Experiments with the CHiME-4 challenge real dataset show significant ASR improvements with an error reduction rate of 12% in the single-channel track and 15% in the 2-channel track, respectively, by using 6-channel beamformed features for the teacher model.