Foundation Models (FMs) have surged in popularity over the past five years, with applications spanning fields from computer vision to natural language processing. Brain-Computer Interfaces (BCIs) have also gained momentum due to their potential to support individuals with complex disabilities. Among BCI paradigms, code-modulated Visual Evoked Potentials (c-VEPs) remain relatively understudied, despite offering high information transfer rates and large selection target capacities. However, c-VEP systems require lengthy calibration sessions, limiting their practicality outside of laboratory settings. In this study, we use a FM for the first time to eliminate the need for lengthy calibration in c-VEP BCI systems. We evaluated two approaches: (1) a truly calibration-free approach requiring no subject-specific data, and (2) a limited calibration approach, where we assessed the benefit of incorporating incremental amounts of calibration data. In both cases, a classification head is trained on data from other subjects. For a new subject, no calibration data is required in the calibration-free setup, making the c-VEP system effectively plug-and-play. The proposed method was tested on two c-VEP datasets. For the calibration-free approach, the average accuracy on the first dataset (n = 17) was 68.8% +/- 17.6%, comparable to the full-calibration performance reported in the original study (66.2% +/- 13.8%), which required approximately 11 minutes of calibration. On the second dataset (n = 12), the calibration-free accuracy was 71.8% +/- 20.2%, versus 93.7% +/- 5.5% from the original study, which required around 3.5 minutes. A limited-calibration approach using only 20% of the subject's data (approximately 43 seconds) yielded 92% +/- 5.2% accuracy. These results indicate that our FM-based approach can effectively eliminate or significantly reduce the need for lengthy calibration in c-VEP BCIs.