Deep Learning (DL)-based code generators have seen significant advancements in recent years. Tools such as GitHub Copilot are used by thousands of developers with the main promise of a boost in productivity. However, researchers have recently questioned their impact on code quality showing, for example, that code generated by DL-based tools may be affected by security vulnerabilities. Since DL models are trained on large code corpora, one may conjecture that low-quality code they output is the result of low-quality code they have seen during training. However, there is very little empirical evidence documenting this phenomenon. Indeed, most of previous work look at the frequency with which commercial code generators (e.g., Copilot, ChatGPT) recommend low-quality code without the possibility of relating this to their (publicly unavailable) training set. In this paper, we investigate the extent to which low-quality code instances seen during training affect the quality of the code generated at inference time. We start by fine-tuning a pre-trained DL model on a large-scale dataset (>4.4M functions) being representative of those usually adopted in the training of code generators. We show that 4.98% of functions in this dataset exhibit one or more quality issues related to security, maintainability, coding practices, etc. We use the fine-tuned model to generate 551k Python functions, showing that 5.85% of them are affected by at least one quality issue. We then remove from the training set the low-quality functions, and use the cleaned dataset to fine-tune a second model which has been used to generate the same 551k Python functions. We show that the model trained on the cleaned dataset exhibits similar performance in terms of functional correctness as compared to the original model (i.e., the one trained on the whole dataset) while, however, generating a statistically significant lower number of low-quality functions (2.16%). Our study empirically documents the importance of high-quality training data for code generators.