Render 4K in H.264 (Quicktime .mov file) in Adobe Premiere

I'm trying to render my files as a .mov file. In Adobe Premiere and Media Encoder I choose "Quicktime" then go down to the codex settings. I see where I can select H.264 (same place where I can choose ProRes, Photo JPEG...etc). When I try on a 4K clip the resolution maxes at 2,000 x 2,000 pixels. If I switch over to Photo JPEG there's no issue--the resolution is 4K.

Here's a screen shot: https://www.dropbox.com/s/vqnkw1jenhxkw3m/Screen%20Shot%202017-05-24%20at%205.44.23%20PM.png?dl=0

Try changing the profile to a higher level. But I never had success rendering H.264 in a Quicktime wrapper at 4K resoltuions. I have to revert to MP4.

A friend of mine who has Final Cut does it all the time--export 4K footage in h.264 with .mov.