It depends on the construction. Solid resin, yes. My Steinberger XL25A was tiny but weighed at least 4kg so they can be on the heavy side. But monocoque design (aka hollow shell such as used by Status and Basslab) are just as strong and much lighter.
Short of snagging a monocoque 6 string Status Streamline or Stealth Mk 2, you will almost certainly be looking at a custom route and that can get very expensive due to the labour costs with creating a set of moulds. One exception, if you aren't wedded to the idea of just carbon is carbon wrapped. One thing to be mindful of is that a pure carbon composite instrument can be unforgivingly brittle sounding and very lively for many. Status injected epoxy foam into their streamline and stealth Mk2 basses to dampen some of those less pleasant resonances. Another way around this is to do a carbon wrapped instrument. This involves wrapping a light weight wood such as cedar in a pre-impregnated composite shell. It saves on labour because moulds are not needed. It's also less complicated to design.
You could approach Jon Shuker with a request for a carbon wrapped instrument. He offers that option with necks on some of the JJ Brunel signature instruments so is very familiar with the technique. And, to my ears at least, the wrapped instruments retain some of the smoother treble and fatter mids of wooden instruments but with all the advantages of carbon composite. The other thing is that Jon could probably accommodate any quirky requests like onboard tuner, specific hardware and pickups, neck dimensions etc. I believe Simon Farmer at GUS uses wrapped wooden cores in his necks too.