An even unimodular 72-dimensional lattice of minimum 8

An even unimodular 72-dimensional lattice $\mathrm{\Gamma }$ having minimum 8 is constructed as a tensor product of the Barnes lattice and the Leech lattice over the ring of integers in the imaginary quadratic number field with discriminant $-7$. The automorphism group of $\mathrm{\Gamma }$ contains the absolutely irreducible rational matrix group $({\text{PSL}}_2(7)\times {\text{SL}}_2(25)):2$.