Multiple codes

2012 1500 Express 4WD 5.7 Hemi

On the way to work the check engine came on. I pulled over and let it sit to check the fluids and they were fine. Took off and 15 miles up the road it started shuttering, mostly under acceleration. It also has a very rough idle. Since I'm not a mechanic, nor have diagnostics, I went to Autozone (the closest). It spit the following: P0304, P1414 and P3497. I pulled the plugs on #4 and they were horrific. I changed them and nothing. Changed the coil pack and still nothing. By the way, I pulled the plugs on #2 to compare and they were clean and a light sandy color.

I am due an oil change that I will do tonight and plugs. I want to wait on the plugs until I figure this out.

When I accelerate quickly, it will smooth out a bit, but once at speed it is certainly missing. Since I don't understand the codes as well as most of you, I'm looking for ideas and guidance. I know that I can always take it to Dodge, but was hoping to use the small checkbook .... not the big one.

Thanks in advance,
Pat

Also wanted to add that when in park, if I rev the engine, it seems to take longer than usual to idle back down.

Well, I now have new plugs, coil, and injector on #4. Still a heavy miss. I'm taking it in next weekend for a compression check. If the compression check were to come back normal, are there any opinions out here?

You might be chasing a wiring problem. Parts swapping is shot gunning a problem like this and money might have more well spent with a technician with proper analyzer and scope equipment.