Iphone 6 plus Touch Screen is Unresponsive When Charging

I just replaced my iPhone 4s with the iPhone 6 plus. I had several issues with the first 6plus and Apple has already replaced the phone once figuring it was a hardware issue. (Actually they couldn't figure out the cause of the issues so as a last resort they replaced the phone.) The second iPhone 6 plus still has an issue with the touch screen becoming unresponsive or erratic while charging. By erratic, I mean that if the phone is unlocked, I try to open my photos but the phone opens facetime. Or I try to open the app store and the phone actually opens the settings. The longer the phone is connected to a power source the more unresponsive or erratic the touch screen becomes. If the phone is locked, I can't even answer an incoming call or unlock the phone. Also, it doesn't matter if the phone is connected to my computer or to an outlet. All connectors (plug and cord) are the ones I received in the box with my iPhone. The only constant is that the phone is connected to a power source. It happens both when the phone is charging and if it has a full 100% charge.

The problem is solved immediately when I disconnect from the power source. If anyone has any ideas on what is causing the issue, I'd appreciate the advice.