A lattice for the PEP-X ultimate storage ring light source[1], having 11 pm-rad natural emittance at a beam energy of 4.5 GeV at zero current, using 90 m of damping wiggler and fitting into the existing 2.2-km PEP-II tunnel, has been recently designed[2]. Such a low emittance lattice requires very strong sextupoles for chromaticity correction, which in turn introduce strong non-linear field effects that limit the beam dynamic aperture. In order to maximize the dynamic aperture we choose the cell phases to cancel the third and fourth order geometric resonances in each 8-cell arc. Four families of chromatic sextupoles and six families of geometric (or harmonic) sextupoles are added to correct the chromatic and amplitude-dependent tunes. To find the best settings of the ten sextupole families, we use a Multi-Objective Genetic Optimizer employing elegant[3] to optimize the beam lifetime and dynamic aperture simultaneously. Then we evaluate dynamic aperture reduction caused by magnetic field multipole errors, magnet fabrication errors and misalignments. A sufficient dynamic aperture is obtained for injection, as well as workable beam lifetime[2]. Show Partial Abstract