Dual symmetry of recently introduced model with quadrupolar and octupolar microscopic interactions [L. Longa, G. Pajak, and T. Wydro, Phys. Rev. E 79, 040701(R) (2009)] is explored in the mean field approximation. Exemplary phase diagrams with new nematic-like phases are shown. Among them is the homogeneous chiral phase, predicted earlier by Landau theory [T. C. Lubensky, L. Radzihovsky, Phys. Rev. E 66, 031704 (2002)].