Just wondering, how did you get grease in your Barrel ??
If you have grease in your barrel, I hope we are talking about something simple like G&G Gear Grease.
Use a Non-Metal aggressive Soap, no Grill Cleaner, Easy Off and so on, Use your Barrel Rod, soft Cloth and warm soapy water, a good dish detergent would probably work best.
Turn the cloth through the barrel, don't just shove it up and down, it´s going to take a while, change your cleaning patches often, and when you are done, give the inside a light coating of Silicon spray, your first 100 rounds are going to be all over the place, so don't even try setting your hop-up.