resources. We demonstrate a superconducting ququart (d = 4) processor and combine quantum optimal control with efficient gate decompositions to implement high-fidelity ququart gates. We distinguish between viewing the ququart as a generalized four-level qubit and an encoded pair of qubits, and characterize the resulting gates in each case. In randomized benchmarking experiments we observe gate fidelities greater 95% and identify coherence as the primary limiting factor. Our results validate ququarts as a viable tool for quantum information processing.