Hi
If you still have the game installed on your Mac then you can try to retrieve the code as follows: http://bluebellflora.com/finding-your-serial-key-using-terminal/
If you no longer have the game installed but previously registered the game either with Origin or on thesims3.com website then you might be able to obtain your code from there - or EA's customer services may be able to access your Origin account and give you the code.
Caspin
