In this paper we propose a method for predicting the status of MGMT promoter methylation in high-grade gliomas. From the available MR images, we segment the tumor using deep convolutional neural networks and extract both radiomic features and shape features learned by a variational autoencoder. We implemented a standard machine learning workflow to obtain predictions, consisting of feature selection followed by training of a random forest classification model. We trained and evaluated our method on the RSNA-ASNR-MICCAI BraTS 2021 challenge dataset and submitted our predictions to the challenge.