The surfaces of eukaryotic cells are decorated with glycans: branched sugar polymers that encode cell identity and play key roles in cell-cell interactions. Eukaryotic glycans are manufactured in the Golgi apparatus, so changes in Golgi organization are expected to impact the glycans made by a cell. We study the Golgi as an information channel whose input is some measure of Golgi perturbation and whose output is the multi-dimensional distribution of cell-surface glycan levels. Specifically, we used the drug Brefeldin A (BFA) to disrupt Golgi organisation, then measured the resulting levels of specific cell-surface glycans in single cells using fluorescently-tagged lectins and flow cytometry. We constructed an optimal Bayesian decoder to infer the input BFA level from single-cell glycan measurements. The decoder has two qualitatively distinct regimes: an all-or-nothing regime that decodes to the minimum and maximum BFA concentrations, and a continuous regime that decodes to intermediate BFA concentrations. We estimate a lower bound of approximately 1 bit for the Shannon information capacity of the Golgi channel in this artificial setting.