A quantum error correcting code is a subspace (codespace) of the state space of a system of n qudits. Logical states are encoded into the codespace so that errors can be detected and corrected. A transversal gate is an operation on encoded states that can be implemented by local operations on the n qudits, i.e., an element of the local unitary group that fixes the codespace. Transversal gates are of special interest because they do not propagate local errors. However, there is no systematic method for finding the transversal gates of a given quantum error correcting code. In this talk, we discuss how to apply Vinberg's theory of graded Lie algebras to determine the group of transversal gates for two special cases: the maximum distance separable codes on four qubits and on three qutrits.