  It follows from classical restrictions on the topology of real algebraic
varieties that the first Betti number of the real part of a real nonsingular
sextic in $\mathbb{CP}^3$ can not exceed $94$. We construct a real nonsingular
sextic $X$ in $\mathbb{CP}^3$ satisfying $b_1(\mathbb{R}X)=90$, improving a
result of F.Bihan. The construction uses Viro's patchworking and an equivariant
version of a deformation due to E.Horikawa.
