Although its most studied and tested forms encompass two-dimensional systems, current quantum platforms technically allow the manipulation of additional quantum levels. We report the first experimental demonstration of a high-dimensional multipartite entangled state in a superconducting quantum processor. We generate the three-qutrit Greenberger-Horne-Zeilinger state by designing the necessary pulses to perform high-dimensional quantum operations. We obtain the fidelity of 78±1%, proving the generation of a genuine three-partite and three-dimensional entangled state. To this date, only photonic devices have been able to create and manipulate these high-dimensional states. Our work demonstrates that another platform, superconducting systems, is ready to exploit high-dimensional physics phenomena and that a programmable quantum device accessed on the cloud can be used to design and execute experiments beyond binary quantum computation.