  The superior computational power promised by quantum computers utilises the
fundamental quantum mechanical principle of entanglement. However, achieving
entanglement and verifying that the generated state does not follow the
principle of local causality has proven difficult for spin qubits in
gate-defined quantum dots, as it requires simultaneously high concurrence
values and readout fidelities to break the classical bound imposed by Bell's
inequality. Here we employ advanced operational protocols for spin qubits in
silicon, such as heralded initialization and calibration via gate set
tomography (GST), to reduce all relevant errors and push the fidelities of the
full 2-qubit gate set above 99%. We demonstrate a 97.17% Bell state fidelity
without correcting for readout errors and violate Bell's inequality with a Bell
signal of S = 2.731 close to the theoretical maximum of 2{\sqrt{2}}. Our
measurements exceed the classical limit even at elevated temperatures of 1.1K
or entanglement lifetimes of 100 {\mu}s.
