  A set of vectors all of which have a constant (non-zero) norm value in an
Euclidean lattice is called a shell of the lattice. Venkov classified strongly
perfect lattices of minimum 3 (R\'{e}seaux et "designs" sph\'{e}rique, 2001),
whose minimal shell is a spherical 5-design. This note considers the
classification of integral lattices whose shells of norm 3 are 5-designs.
