I don’t know the technical details about this forum’s software setup, but it seems to me like it’s having the exact same issue as: http://pento.net/2014/04/07/wordpress-and-utf-8/ (in short: the database’s encoding does not support characters not in Unicode’s BMP and cuts off posts as a result).
It affects any character outside BMP not just emoji. Actually thanks to emoji many software now has better Unicode support as software developers can’t dismiss requests to support characters outside BMP as being exotic anymore.
Comments
Edit: Looks like it happens if I try to paste the actual emoji character instead of the :code: form
http://emoji.codes/family
:code: form is called "shortcode"