Welcome to FTE. What are you using to pull the codes? The free scans at the parts stores won't read the engine codes in these trucks. Can you describe the rough running a little better? Does it feel like a miss, or like the engine is not firing on all cylinders?

If the CEL (check engine light) comes on, there is a code there. You just need the right kind of code reader to see it. This kind of sounds like a loose UVCH (under valve cover harness) issue. When things heat up, the connection gets worse. If you have an ohm meter handy, read through this thread that has pictures and the test procedure so you understand what you're looking for. https://www.ford-trucks.com/forums/8...ck-shakes.html

Come back and let us know what the test shows.