Particle cascades initiated by ultrahigh energy neutrinos in the lunar regolith will emit an electromagnetic pulse with a time duration of the order of nanoseconds through a process known as the Askaryan effect. It has been shown that in an observing window around 150 MHz there is a maximum chance for detecting this radiation with radio telescopes commonly used in astronomy. In 50 h of observation time with the Westerbork Synthesis Radio Telescope array we have set a new limit on the flux of neutrinos, summed over all flavors, with energies in excess of 4x10(22) eV.