Neural program embeddings have demonstrated considerable promise in a range of program analysis tasks, including clone identification, program repair, code completion, and program synthesis. However, most existing methods generate neural program embeddings di-rectly from the program source codes, by learning from features such as tokens, abstract syntax trees, and control flow graphs. This paper takes a fresh look at how to improve program embed-dings by leveraging compiler intermediate representation (IR). We first demonstrate simple yet highly effective methods for enhancing embedding quality by training embedding models alongside source code and LLVM IR generated by default optimization levels (e.g., -02). We then introduce IRGEN, a framework based on genetic algorithms (GA), to identify (near-)optimal sequences of optimization flags that can significantly improve embedding quality. We use IRGEN to find optimal sequences of LLVM optimization flags by performing GA on source code datasets. We then extend a popular code embedding model, CodeCMR, by adding a new objective based on triplet loss to enable a joint learning over source code and LLVM IR. We benchmark the quality of embedding using a rep-resentative downstream application, code clone detection. When CodeCMR was trained with source code and LLVM IRs optimized by findings of IRGEN, the embedding quality was significantly im-proved, outperforming the state-of-the-art model, CodeBERT, which was trained only with source code. Our augmented CodeCMR also outperformed CodeCMR trained over source code and IR optimized with default optimization levels. We investigate the properties of optimization flags that increase embedding quality, demonstrate IRGEN's generalization in boosting other embedding models, and establish IRGEN's use in settings with extremely limited training data. Our research and findings demonstrate that a straightforward addition to modern neural code embedding models can provide a highly effective enhancement.