The Ekert quantum key distribution protocol uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol uses instead pairs of entangled qutrits to achieve better noise resistance than the Ekert protocol. It performs checks based on a Bell inequality for qutrits named CHSH-3. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but achieves even better noise resistance than 3DEB. This gain of performance is obtained by using another inequality called here hCHSH-3. As the hCHSH3 inequality involve products of observables which become incompatible when using quantum states, we show how the parties running the protocol can measure the violation of hCHSH3 in the presence of noise, to ensure the secrecy of the key.