Information in the nervous system is encoded by the spiking patterns of large populations of neurons. The analysis of such high-dimensional data is typically restricted to simple, arbitrarily defined features like spike rates, which discards information in the temporal structure of spike trains. Here, we use a recently developed method called SpikeShip based on optimal transport theory, which captures information from all the relative spike-timing relations among neurons. We compared spike-rate and spike-timing codes in neural ensembles from six visual areas during natural video presentations. Temporal spiking sequences conveyed substantially more information about natural movies than population spike-rate vectors, especially for larger number of neurons. As previously, shown, population rate vectors exhibited substantial drift across repetitions and between blocks. Conversely, encoding through temporal sequences was stable over time, and did not show representational drift both within and between blocks. These findings reveal a stable neural code based on precise relative spike timing relations in high-dimensional neural ensembles.