Congrats on the new chariot. Yours is the same age as mine though you're at half the mileage. The exhaust back pressure code comes up a lot in conjunction with other problems. I would try replacing the sensor but you might find that is merely a symptom, not a cause. Check the vacuum lines that are on top of the turbo in the heat shield that is clipped over them with two push buttons. My vac lines were very bad in that section. A smoke test might be in order as well.

Good luck with the trouble shooting!

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2003 4.4i black ext./black int./black headliner (kid's runabout)
2014 535d X-drive, M package, silver/black interior

Sold but not forgotten:
2009 E70 35d, black ext./black int./black headliner (sold 2021)
2006 4.8iS Le Mans blue/cream int./black headliner, SOLD in 2012 sadly...

Other hardware:
2015 Cayenne S (wife's new DD and definitely wroooommmmm)
2016 Tundra 1794 edition crew cab, luxo hauler
2005 Tundra crew cab, weekend hauler. Sold after 150k very happy miles.