Context: Code readability plays a critical role in software maintenance and evolvement, where a metric for classifying code readability levels is both applicable and desired. However, most prior research has treated code readability classification as a binary classification task due to the lack of labeled data. Objective: To support the training of multi-class code readability classification models, we propose an enhanced data augmentation approach. Method: The approach includes the use of domainspecific data transformation and GAN-based data augmentation. By virtue of this augmentation approach, we could generate sufficient readability data and well train a multi-class code readability model. Result: A series of experiments are conducted to evaluate our augmentation approach. The experimental results show that a state-of-the-art multi-class code readability classification accuracy of 68.0% is reached with a significant improvement of 6.3% compared to only using the original data. Conclusion: As an innovative work of proposing multi-class code readability classification and an enhanced code readability data augmentation approach, our method is proved to be effective.