I know it's not carbon and not what you're looking for but it'd be light...I have a X-Lite Ti one that needs recycling somehow. Postage costs is enough for it.
After my 'off the top of the head' offer; I'll just chuck in some more info re these X-Lite ti bars I have:
They're usual grey stock, maybe a 3deg sweep.Logos are faded out. 550mm long..
BUT with a 130mm long crack running along where the right hand hand grip would be and clamp compression damage. Ready for the skip, clever use as a component mount or use as..a wind chime?