I also am using PoEdit to make my .mo files but you still need to get a based .po file to be able to create your translation.
One solution is to use the already existing file located in \modules\core\po\ then you edit it in PoEdit.
Once the edit is done, the program -will- create a .mo file right in the same directory named pl_PL.mo (i think it's the polish code but not quite sure there)
If the program doesn't create it when you hit save, it means you have some error in your file (like funny character and the sort) 
When you are satisfied with the translation and ready tio use it, just rename the .mo file into modules_core.mo and place it in \modules\core\locale\pl_PL\LC_MESSAGES
Let us know if you still have issue.
PS: sometimes, you need to reboot the webserver for the .mo file to be applyed (not always but it happens)
See you
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The Termite
