Lists all the TPE's that teams have. Barbosa is owed $7.6M (according to Hoopshype). So using a TPE (and TPE alone), the only two teams that can take on Barbosa's contract (without having to trade players) are LAL and Utah.
If Utah continues to play well (which is doubtful, but still), they may want to make a playoff push with Barbosa. Utah does not have their own 1st round pick (traded to Minny), but they have GSW's (top 7 protected). I wonder if Utah would be willing to trade that pick for Barbosa at the trade deadline? They could use the depth at both PG and SG as that's their big weakness. But that might be asking for too much. GSW's pick could be pretty good in a deep draft, and Utah may not want to trade that for a rental.
Of course you could also trade him to teams like Indiana who have the cap space, as you suggested.