Yes, a code is required to access the online of Mass Effect 3. Many games are doing this recently, EA Games has made it mandatory on all of their released games. Unfortunately, a code only comes free with a new copy of the game. You can purchase a code for ~$10 on the xbox marketplace. Also, if you decide to purchase the game from GameFly, they will send you a new copy of the case as well as all contents originally inside the box (that includes a new code!).
Hope this helps