  An even unimodular 72-dimensional lattice $\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 $\Gamma $ contains the absolutely
irreducible rational matrix group $(\PSL_2(7) \times \SL _2(25)) : 2$.
