Code-modulated visual evoked potentials (c-VEP) are a promising control signal for non-invasive brain-computer interfaces (BCI). Previous studies showed that this paradigm can reach higher performance and reliability than previous approaches, such as P300 potentials or steady-state visual evoked potentials. However, a calibration phase is still needed before starting to use the system, which limits the applicability of the technology. In this exploratory study, our goal is to eliminate the need for this calibration phase to improve the usability of c-VEP-based BCIs. To this end, we designed, developed, and tested a new bitwise reconstruction strategy that takes advantage of deep learning and transfer learning to overcome inter-subject variability. We tested the method on a database of 10 subjects that included recordings with binary (i.e., black and white) and non-binary (i.e., 5 shades of gray) stimulation paradigms to reduce eyestrain. Results show that the proposed method reaches a maximum average accuracy of 95% using 9 stimulation cycles without calibration. These results represent a promising step forward towards more practical c-VEP-based BCIs.