The Unified Modeling Language is a standardized visual language widely used for modeling and documenting the design of software systems. Although many tools generate UML diagrams from UML code, generating executable UML code from image-based UML diagrams remains challenging. This paper proposes a new approach to generate UML code using a large multimodal language model automatically. Synthetic UML activity and sequence diagram datasets were created to train and test the model. We compared standard fine-tuning with LoRA techniques to optimize base models. The experiments measured code generation accuracy across different model sizes and training strategies. These results demonstrated that domain-adapted MM-LLMs perform for UML code generation automation, whereby, at the best model, it achieved BLEU and SSIM scores of 0.779 and 0.942 on sequence diagrams. This will enable the modernization of legacy systems and decrease the manual effort in software development workflows.