Error-correcting codes protect messages by making valid messages different from one another. Their minimum distance counts the fewest symbol changes separating two valid messages. A large distance provides room to detect or correct corruption. Algebraic symmetry can make a code compact to describe. But this research candidate shows that one particular kind of symmetry can also impose a hidden weakness. The paper studies codes built from modular group algebras, with especially clear examples based on binary addition. Its first argument finds a whole subcode confined to a small set of coordinates. That forces an upper limit on the original code’s minimum distance. For a matrix of order eight over the eight-element field, the limit is seven, and an older construction attains it. The broader result concerns what happens as the codes grow. Under precise assumptions, with the field and number of coordinate blocks fixed, free modular codes can keep a positive information rate while their relative minimum distance tends to zero. Here free describes their algebraic module structure, not a lack of constraints. This is not a claim that all symmetric codes are poor, or that coding theory has reached a universal limit. Nonfree codes outside the stated assumptions remain outside the theorem. The proof concentrates coefficient sums into one quotient fibre, producing a low-weight codeword. The binary scalar case has an important predecessor in Charpin’s work. The proposed extensions concern vector coefficients, every prime characteristic and module-level bounds. The package provides written proofs, exact checkers, explicit certificates and deliberately corrupted cases that the checker must reject. The result remains an unrefereed candidate, with incomplete historical priority clearance and no formal proof-assistant verification. This is Evidence Press, modular-code obstructions, released on the twenty-ninth of September twenty twenty-six. The paper and evidence are linked here. This synthetic AI voice explains the research; it is not additional scientific evidence.