B737 Captain reported encountering wake turbulence in trail of an A320 on climb-out of LAX.

Narrative

On climb out of LAX going to ZZZ we were following who we believed to be Aircraft Y. The FO was hand flying and I was PM. We had received the first bit of wake turbulence about 1;000 to 2;000 feet. We both remarked that it seemed bizarre seeing as how it looked to be good separation between departures and that we were following an A320. However at 4;000+ feet we started the second left hand on the SID and were previously cleared to climb higher. Flaps were fully retracted and the FO was slowly accelerating to 250 (airspeed was around 230 at the time) in the left hand turn we received another good bounce from wake turbulence and the FO exceeded the bank to about 32 degrees left not much farther than the Flight Director (FD) was indicating. We received another aural 'bank angle' only once; I exclaimed 'check path' as I saw him correcting back; and with the aural there seemed to be no need to repeat the obvious 'bank angle' call. The wake lasted another 10 seconds and the rest of the flight was uneventful.