The time delay of a light signal in the quadrupole field of a body at rest is determined in the second post-Newtonian (2PN) approximation in harmonic coordinates. For grazing light rays at the Sun, Jupiter, and Saturn the 2PN quadrupole effect in time delay amounts up to 0.004, 0.14, and 0.04 picosecond, respectively. These values are compared with the time delay in the first post-Newtonian (1PN and 1.5PN) approximation, where it turns out that only the first eight mass multipoles and the spin dipole of these massive bodies are required for a given goal accuracy of 0.001 picosecond in time delay measurements in the solar system. In addition, the spin-hexapole of Jupiter is required on that scale of accuracy.