Is it possible to download a compatible version of Xcode on a mac running this version OS?
Xcode on 10.11.6
Yes - restrictions apply.
Try 8.2.1 - search here: https://developer.apple.com/download/more/ (may require a paid Developer Program account).
Details via xcode wiki
yes It is possibl.
Accessing 'more downloads' may require a paid Developer Program account.