I was having problems with The Beast, my '06 Grand Vitara, 670 & 243 codes kept coming up, we changed various parts, checked for exhaust leaks etc. Turns out it could have been the hose to the turbo that was the problem. After everything Beast is now grounded, everything is ticking fine, it has been the hose that is the problem.
So if you have an issue with either of those codes, check that particular hose.