Let \(S\) be a surface of general type; the maximum possible value of the degree \(d\) of the canonical map of \(S\) is 36, and very recently an example where this maximum is achieved was given in [S.-K. Yeung, Math. Ann. 368, No. 3–4, 1171–1189 (2017; Zbl 1390.14119)]. Here the author constructs an example with \(d=24\), which was the record at the time when the paper was written. The surface \(S\) of the example has geometric genus \(h^0(S,\omega_S)=3\), irregularity \(h^0(S,\Omega^1_S)=0\) and \(K_S^2=24\). It is constructed as the minimal desingularization of a \(\mathbb Z_2^4\)-cover of the plane, branched over a very special configuration of singular curves, whose existence is shown by computer aided computations.