Here are two new codes from April 2016. You can enter codes either at the beginning when you first login or later with the settings menu.
Here they are:
explore – 500 gems
trench – 500 gems
Type in the codes above and you will get 500 gems apiece. Codes can be used once each for each account.
For a full list of the codes available, visit http://animaljamcodesfree.com
The codes on this page are up to date; none are expired and they all work.
If anyone knows of any code not on the list, please leave the info in the comments.