Just shared a short video over on my Instagram with the GH4 balanced on my modified CAME 6000 2 Axis Gimbal. I've uploaded a copy to my YouTube channel seen below. I chose the Rokinon 7.5mm fisheye as it's lightweight and I can correct some distortion to simulate a UWA (ultra wide angle) lens when shooting in 4K mode.
Instagram Video GH4 2 Axis Video Gimbal
Absolutely no issues getting this camera balanced on the CAME 6000, and this is a ready-to-run gimbal system with no programming or assembly necessary (find it here). Just charge the batteries, balance and go. Mine was modified with side handles, but shortly after my modification they now offer these side handles as a standard.
Of course you won't have the third axis (Pan stabilization) which is extremely helpful as you walk swiftly or run. If you just plan on stabilizing your handheld shots free from rolling shutter and keeping the horizon level, this compact super lightweight carbon gimbal works perfectly.