The isocitrate dehydrogenase (IDH) gene mutation is an essential biomarker for the diagnosis and prognosis of glioma. It is promising to better predict glioma genotype by integrating focal tumor image and geometric features with brain network features derived from MRI. Convolutional neural networks show reasonable performance in predicting IDH mutation, which, however, cannot learn from non-Euclidean data, e.g., geometric and network data. In this study, we propose a multi-modal learning framework using three separate encoders to extract features of focal tumor image, tumor geometrics and global brain networks. To mitigate the limited availability of diffusion MRI, we develop a self-supervised approach to generate brain networks from anatomical multi-sequence MRI. Moreover, to extract tumor-related features from the brain network, we design a hierarchical attention module for the brain network encoder. Further, we design a bi-level multi-modal contrastive loss to align the multi-modal features and tackle the domain gap at the focal tumor and global brain. Finally, we propose a weighted population graph to integrate the multi-modal features for genotype prediction. Experimental results on the testing set show that the proposed model outperforms the baseline deep learning models. The ablation experiments validate the performance of different components of the framework. The visualized interpretation corresponds to clinical knowledge with further validation. In conclusion, the proposed learning framework provides a novel approach for predicting the genotype of glioma.