You could be told to pay all of the credit card and you could get sanctioned if your ex finds this out. Just pay it off. It will probably be cheaper then if you litigate it and suffer more damaging consequences.
From reading your facts it appears he had knowledge of the account, you stated that he used the account as well. Did he list it on his schedule of assets and debts? If so that helps to defend you against allegations that you sought to hide debt from him that you acquired in his name during marriage.
However, the debt appears not to have been addressed in the settlement. Generally, community debt is owed 50/50 by both parties. The credit card company won't care who is going to pay, they just want their money back.
If you are on speaking terms with your ex why not talk to him about this debt and seeing if you can come to an agreement to both pay half. If so, draft up a "Stipulation and Order" and both sign it and file with the court for signature.