Brain–computer interfaces (BCIs) enable direct communication between the brain and external devices. BCIs based on code-modulated visual evoked potentials (cVEPs) utilize predefined code sequences to generate distinct visual stimuli, evoking characteristic responses in the occipital region. This paradigm enables intuitive target selection by identifying which stimulus the user is looking at, but accurate classification is impeded by temporal overlap, morphological variability, and individual differences. Traditional methods generally apply static channel weights and offer limited interpretability of electrode contributions. We propose a Graph-Attentive Convolutional Neural Network (GAT-CNN) that promotes the dynamic re-weighting of electrode channels throughout the cVEP response and provides interpretable measures of electrode importance. Evaluated on 30 participants, our model achieved a mean window-wise accuracy of 89% in predicting the observed cVEP stimuli at 3.9 ms resolution (1/256 s) using 66 ms data windows, and revealed trends in electrode significance. These results aim to demonstrate the feasibility of a high-performance, low-latency, and individually tailored cVEP-BCI.