This paper presents accurate absolute positions from a 24 GHz Very Long Baseline Array (VLBA) search for compact extragalactic sources in an area where the density of known calibrators with precise coordinates is low. The goals were to identify additional sources suitable for use as phase calibrators for galactic sources, determine their precise positions, and produce radio images. In order to achieve these goals, we developed a new software package, PIMA, for determining group delays from wide-band data with much lower detection limits. With the use of PIMA, we have detected 327 sources out of 487 targets observed in three 24 hr VLBA experiments. Among the 327 detected objects, 176 are within 10° of the Galactic plane. This VGaPS catalog of source positions, plots of correlated flux density versus projected baseline length, contour plots, as well as weighted CLEAN images, and calibrated visibility data are available on the Web in FITS format. Approximately one-half of objects from the 24 GHz catalog were observed at dual-band 8.6 GHz and 2.3 GHz experiments. Position differences at 24 GHz versus 8.6/2.3 GHz for all but two objects on average are strictly within reported uncertainties. We found that for two objects with complex structures, positions at different frequencies correspond to different components of a source.