B767 Captain reported they turned the incorrect direction on initial climb and when correcting exceeded 30 degrees of bank; resulted in two bank angle warnings.

Narrative

Aircraft X was cleared on the ZZZZZ departure from ZZZZ. Takeoff was uneventful. After contacting Departure Control; we were given a heading of 230 degrees. Because we were beginning a left turn and because the departure continued to the left with a first fix to the left; I assumed the clearance was a left turn. After initiating a left turn; the controller clarified that the turn was intended to be a right turn to heading 230. He used the terminology of 'heading 230 by the right'. We complied on continued the departure. During the right turn; the PF exceeded 30 degrees of bank and we received a bank angle warning twice. His perception was that we needed to expedite the turn to the right. After we leveled off; we debriefed the event in accordance with company procedure. I identified that I should have asked for clarification of the clearance if there was doubt as to what was transmitted. I also emphasized the importance of remaining aware of the flight envelope limitations even if there is a possible ATC deviation.