Neural networks that can capture key principles underlying brain computation offer exciting new opportunities for developing artificial intelligence and brain-like computing algorithms. Such networks remain biologically plausible while leveraging localized forms of synaptic learning rules and modular network architecture found in the neocortex. Compared to backprop-driven deep learning approches, they provide more suitable models for deployment of neuromorphic hardware and have greater potential for scalability on large-scale computing clusters. The development of such brain-like neural networks depends on having a learning procedure that can build effective internal representations from data. In this work, we introduce and evaluate a brain-like neural network model capable of unsupervised representation learning. It builds on the Bayesian Confidence Propagation Neural Network (BCPNN), which has earlier been implemented as abstract as well as biophyscially detailed recurrent attractor neural networks explaining various cortical associative memory phenomena. Here we developed a feedforward BCPNN model to perform representation learning by incorporating a range of brain-like attributes derived from neocortical circuits such as cortical columns, divisive normalization, Hebbian synaptic plasticity, structural plasticity, sparse activity, and sparse patchy connectivity. The model was tested on a diverse set of popular machine learning benchmarks: grayscale images (MNIST, F-MNIST), RGB natural images (SVHN, CIFAR-10), QSAR (MUV, HIV), and malware detection (EMBER). The performance of the model when using a linear classifier to predict the class labels fared competitively with conventional multi-layer perceptrons and other state-of-the-art brain-like neural networks.