Color quantization (CQ) is one of the most common and important procedures to be performed on digital images. In this paper, a new approach to hierarchical color quantization is described, presenting a novel neural network architecture integrated by a convolutional autoencoder and a Growing Hierarchical Bregman Neural Gas (GHBNG). GHBNG is a CQ algorithm that allows the compression of an image by choosing a reduced set of the most representative colors to generate a high-quality reproduction of the original image. In the technique proposed here, an autoencoder is used to translate the image into a latent representation with higher per-pixel dimensionality but reduced resolution, and GHBNG is then used to quantize it. Experimental results confirm the performance of this technique and its suitability for tasks related to color quantization.