Ok, the mysql fulltext search index was set to the default of 4 characters minimal length, and the settings from XenForo do not touch that.
I changed it to 3 and rebuild the index on our test forum instance and it looks good, we will integrate this changes on the real (this) forum after a few tests.
Edit: It's now enabled on the production forum, search for 3 character words should be a lot better now.