The ultimate goal of brain-computer interfaces (BCIs) based on visual modulation paradigms is to achieve high-speed performance without the burden of extensive calibration. Code-modulated visual evoked potential-based BCIs (c-VEP-BCIs) modulated by broadband white noise (WN) offer various advantages, including increased communication speed, expanded encoding target capabilities, and enhanced coding flexibility. However, the complexity of the spatial-temporal patterns under broadband stimuli necessitates extensive calibration for effective target identification in c-VEP-BCIs. Consequently, the information transfer rate (ITR) of c-VEP-BCI under limited calibration usually stays around 100 bits per minute (bpm), significantly lagging behind state-of-the-art steady-state visual evoked potential-based BCIs (SSVEP-BCIs), which achieve rates above 200 bpm. To enhance the performance of c-VEP-BCIs with minimal calibration, we devised an efficient calibration stage involving a brief single-target flickering, lasting less than a minute, to extract generalizable spatial-temporal patterns. Leveraging the calibration data, we developed two complementary methods to construct c-VEP temporal patterns: the linear modeling method based on the stimulus sequence and the transfer learning techniques using cross-subject data. As a result, we achieved the highest ITR of 250 bpm under a minute of calibration, which has been shown to be comparable to the state-of-the-art SSVEP paradigms. In summary, our work significantly improved the c-VEP performance under few-shot learning, which is expected to expand the practicality and usability of c-VEP-BCIs.