A limitation of brain-computer interface (BCI) spellers is that they require the user to be able to move the eyes to fixate on targets. This poses an issue for users who cannot voluntarily control their eye movements, for instance, people living with late-stage amyotrophic lateral sclerosis (ALS). This pilot study makes the first step towards a gaze-independent speller based on the code-modulated visual evoked potential (c-VEP). Participants were presented with two bi-laterally located stimuli, one of which was flashing, and were tasked to attend to one of these stimuli either by directly looking at the stimuli (overt condition) or by using spatial attention, eliminating the need for eye movement (covert condition). The attended stimuli were decoded from electroencephalography (EEG) and classification accuracies of 88% and 100% were obtained for the covert and overt conditions, respectively. These fundamental insights show the promising feasibility of utilizing the c-VEP protocol for gaze-independent BCIs that use covert spatial attention when both stimuli flash simultaneously.