You can just redeem the code on your browser on the computer and then just go to download history on the Xbox to download it. Picture related. Unless you mean you can't play it of course, then that's a whole other ballgame.
That would work if they aren't region blocking it - I couldn't get the Gears 3 demo with a code through this method because they blocked japan IPs... you might be able to start a region blocked item with a browser code claim, but it will ultimately fail to download (probably around 98~99%). You _can_ proxy your xbox on the last 2% of the download to a supported region, but it's probably not worth the effort. :/