Footnotes to a footnote of a paper by Fano

Following a suggestion in a footnote of the paper \cite {Fa} by Fano, we give a direct proof of the fact that one of the two Fano threefolds of maximal degree 72 in ${\text{p}}^{38}$ is isomorphic to the anticanonically embedded weighted projective space $\text{p}(1,1,4,6)$.