Today, machine learning tools, particularly artificial neural networks, have become crucial for diverse applications. However, current digital computing tools to train and deploy artificial neural networks often struggle with massive data sizes and high power consumptions. Optical computing provides inherent parallelism accommodating high-resolution input data and performs fundamental operations with passive optical components. However, most of the optical computing platforms suffer from relatively low accuracies for machine learning tasks due to fixed connections while avoiding complex and sensitive techniques. Here, we demonstrate a genetically programmable yet simple optical neural network to achieve high performances with optical random projection. By genetically programming the orientation of the scattering medium which acts as a random projection kernel and only using 1% of the search space, our novel technique finds an optimum kernel and improves initial test accuracies by 8-41% for various machine learning tasks. Through numerical simulations and experiments on a number of datasets, we validate the programmability and high-resolution sample processing capabilities of our design. Our optical computing method presents a promising approach to achieve high performance in optical neural networks with a simple and scalable design.