On minimal coset covering of solutions of a boolean equation

For the equation $x_1x_2\dots x_n+x_{n+1}x_{n+2}\dots x_{2n}+x_{2n+1}x_{2n+2}\dots x_{3n}=1$ over the finite field $F_2$ we estimate the minimal number of systems of linear equations over the same field such that the union of their solutions exactly coincides with the set of solutions of the equation. We prove in this article that the number in the question is not greater than $9n^{\log_2^3}+4.$