Discrete visual tokenizers translate images into ordered sequences of codes, providing a natural representation for structural description of scenes. Yet existing adaptive tokenizers either require post-hoc search or select among a discrete set of pre-trained rates, rather than learning a continuous per-image sequence length coupled to the model and scene, and they typically train against pixel reconstruction, emphasizing texture rather than structure. We propose STROP, a discrete visual tokenizer architecture that forms structural scene representations and simultaneously learns how long an image's visual program should be. Using a four-phase curriculum supervised by local rate--distortion probes against frozen DINOv3 features, STROP optimizes a dedicated length head that estimates the active prefix length in a single forward pass. By bypassing pixel-level reconstruction gradients, the codebook is shaped entirely by the quality of higher-level latent representations. Program length grows with scene complexity, and signs of compositional structure emerge both in downstream dense-prediction transfer and in direct inspection of the learned code vocabulary.