I had this very same issue earlier. Let me quote someone who assisted me earlier with this.

"That sounds like the error codes for the version check error. If you go to your game folder in /SquareEnix/Final Fantasy XIV: A Realm Reborn/ and replace your boot folder with a known working one (linked below) that usually resolves this issue.

Boot folder: https://www.dropbox.com/s/dy6douu7m0ofuot/boot.rar "

After I downloaded the boot folder and replaced it the launcher got pasted the version check. Sadly though I cannot seem to finish downloading the update. Hope it works for you.