Molecule have UV response.
  How much UV response? (the devil is in the details).
0.04ppm is approximately 40 ng/mL. If you have a high extinction coefficient (say, 10^4 or so), then your UV detection limit will be around the nanogram level. If your diluent is much weaker than your mobile phase, then you may be able to get away with a large injection volume (several hundred microliters). 
If your molecule fluoresces, you should be able to work with a much smaller injection volume (fluorescence detection is typically at least an order of magnitude more sensitive than UV). If it can be oxidized or reduced easily, then an electrochemical detector will let you do the same.