Are you entering the code through the eshop? As codes with Z in will not be accepted through the eshop unlike what the GAME website says and from other sources too....my code also contains a Z for example.
SOLUTION: Try going onto your Pokemon game and entering through mystery gift instead on the start up screen - this will accept the Z in the code.
Other issues can include:
A bad internet connection (try again within a few hours)
You have a game which does not accept the Shiny Charizard code. Games which accept the code are X, Y , Omega Ruby and Alpha Sapphire.
You need to update both your 3DS system and your Pokemon game.