If the game was purchased recently, try reloading your games library via the main menu (2nd entry: Reload my games) or click the refresh icon in the top left of your games library. Origin requires a restart or refresh of your games library before if will show product codes on the game details page after a purchase.
Hope that works for you. If not, please contact a Game Advisor at https://help.ea.com/contact-us and they will be able to provide you with your code.
Should you still have issues with the code, contact Customer Service/Game Advisors.
Here's how:
1 Click on the following link: https://help.ea.com/contact-us
2 Make sure you are logged in (top right corner)
3 Click on the blue button "Contact a Game Advisor"
4 Enter the name of your game or product (or "Origin" for account-related issues) and click "Find Solutions"
5 Select the type of issue and the platform you play on, and click on "Find Solutions".
6 Click on the blue button "I still need help" if the FAQ articles do not apply to your situation.
7 Select a contact option. Note that you may get different contact options depending on your country.
