How to make a 40mH inductor
Hmm, trolling digikey it looks like anything over ~10mH has a SRF above or near your working frequency.  Maybe a few 10mH in series.  Since I assume you are "resonating" your ~10-100pF antenna some inductor with "taps" might be useful.    As a crazy idea how about an opamp gyrator circuit.  (I've never made one, but always wanted to.)  I'm guessing you'd want a fairly fast opamp, maybe an AD825.