The ultra-diffuse galaxies DF2 and DF4 in the NGC 1052 group share several unusual properties: they both have large sizes1, rich populations of overluminous and large globular clusters2-6, and very low velocity dispersions that indicate little or no dark matter7-10. It has been suggested that these galaxies were formed in the aftermath of high-velocity collisions of gas-rich galaxies11-13, events that resemble the collision that created the bullet cluster14 but on much smaller scales. The gas separates from the dark matter in the collision and subsequent star formation leads to the formation of one or more dark-matter-free galaxies12. Here we show that the present-day line-of-sight distances and radial velocities of DF2 and DF4 are consistent with their joint formation in the aftermath of a single bullet-dwarf collision, around eight billion years ago. Moreover, we find that DF2 and DF4 are part of an apparent linear substructure of seven to eleven large, low-luminosity objects. We propose that these all originated in the same event, forming a trail of dark-matter-free galaxies that is roughly more than two megaparsecs long and angled 7° ± 2° from the line of sight. We also tentatively identify the highly dark-matter-dominated remnants of the two progenitor galaxies that are expected11 at the leading edges of the trail.