Recent theories have proposed that the unifying principle of brain function is the minimisation of variational free energy and that this is best achieved using a hierarchical predictive coding (HPC) framework. Hierarchical Temporal Memory (HTM) is a model of neocortical function that fits within the free energy framework but does not implement predictive coding. Recent work has attempted to integrate predictive coding and hierarchical message passing into the existing suite of HTM Cortical Learning Algorithms (CLA) producing a PC-CLA hybrid. In this paper we examine for the first time how such hierarchical message passing can be implemented in a pure HTM framework using distal dendrite structures that are already implemented in the CLA temporal pooler. We show this approach outperforms the more simplistic proximal dendrite structures used in the PC-CLA hybrid and also that the new CLA hierarchy is effective for anomaly detection and image reconstruction problems that are beyond the reach of the existing single-level CLA framework.