Currently there are 8 native SuperZoom lenses for Panasonic GH4 and all of these lenses are autofocus (AF) type.
Panasonic GH4 doesn't have a sensor based image stabilization system but 4 of these SuperZoom lenses features optical image stabilization.
Since Panasonic GH4 has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 4 SuperZoom lenses with Weather Sealings.