We present ongoing work on a new automatic code generation approach for supporting quantized generative inference on LLMs such as LLaMA or OPT on off-the-shelf CPUs. Our approach is informed by the target architecture and a performance model, including both hardware characteristics and method-specific accuracy constraints. Results on CPU-based inference for LLaMA models show that our approach can lead to high performance and high accuracy, comparing favorably to the best existing open-source solution.