We show the first use of generative transformers for generating calorimeter showers as point clouds in a high-granularity calorimeter. Using the tokenizer and generative part of the OmniJet-$α$ model, we represent the hits in the detector as sequences of integers. This model allows variable-length sequences, which means that it supports realistic shower development and does not need to be conditioned on the number of hits. Since the tokenization represents the showers as point clouds, the model learns the geometry of the showers without being restricted to any particular voxel grid.