A friend has an '03 Heritage and had a similar problem. The fuel line that is in the tank rubbed and developed a hole and caused missing etc.

 

I'm having the same issue on my '07 deuce. I cleared the codes as they may not have been cleared from a previous issue. I changed plugs as it was time, drained fuel and put in known good fuel. It started on the road at 7500 elevation I thought it was bad gas as I was down to about 1/4 tank. When I got to gas station filled with chevron 91 and it ran fine, now I drained and put in 2 gallons good and still reads out P0152 code rear o2 sensor rich which explains the miss and backfire into throttle body. I'm starting to think that the fuel filter and or fuel pump as it was fine when I filled up. I'm going to fill tank again and see if that clears it and then it will be my guess of a fuel pump/filter. Anyone else have this???

 

For the 0152 code, sensor rich, probably a bad sensor. The miss and lean pop mean that the fuel trim is leaning to compensate for the rich indication of a bad sensor. I would be inclined to inspect/replace the offending o2 sensor and see if it fixes it. Inspect the harness for it too, since a short to a voltage source could give a rich indication, along with a bad ECM being another possible cause.