We report the results of an experimental search for ultralight axionlike dark matter in the mass range 162-166 neV. The detection scheme of our Cosmic Axion Spin Precession Experiment is based on a precision measurement of ^{207}Pb solid-state nuclear magnetic resonance in a polarized ferroelectric crystal. Axionlike dark matter can exert an oscillating torque on ^{207}Pb nuclear spins via the electric dipole moment coupling g_{d} or via the gradient coupling g_{aNN}. We calibrate the detector and characterize the excitation spectrum and relaxation parameters of the nuclear spin ensemble with pulsed magnetic resonance measurements in a 4.4 T magnetic field. We sweep the magnetic field near this value and search for axionlike dark matter with Compton frequency within a 1 MHz band centered at 39.65 MHz. Our measurements place the upper bounds |g_{d}|<9.5×10^{-4} GeV^{-2} and |g_{aNN}|<2.8×10^{-1} GeV^{-1} (95% confidence level) in this frequency range. The constraint on g_{d} corresponds to an upper bound of 1.0×10^{-21} e cm on the amplitude of oscillations of the neutron electric dipole moment and 4.3×10^{-6} on the amplitude of oscillations of CP-violating θ parameter of quantum chromodynamics. Our results demonstrate the feasibility of using solid-state nuclear magnetic resonance to search for axionlike dark matter in the neV mass range.