  We prove that the smallest distance 3 Quantum Error Correcting Code with a
transversal gate outside the Clifford group is the well-known 15-qubit
Reed-Muller code, also known as a tri-orthogonal code. Our result relies on
fewer assumptions than previous works. We further extend this result by finding
the minimal code that also possesses any other non Clifford transversal
single-qubit gate.
