For Blizzard shop pre-orders, the beta is automatically applied to the account, no additional codes are needed. If this is not appearing for install, try clearing the cache and tools folder for the Blizzard Application.
For physical pre-orders or Twitch drops for beta access and the beta code was not received, please contact the retailer. These can be claimed on the Call of Duty website.
Additional information for the Modern Warfare Beta can be found here.