It depends upon the situation.

If you have a debt and unpaid for so long and your bank has filed a charge against you then you wont be able to get the visa ( if you are outside Qatar )

if you are in Qatar, and you want to renew your visa and the bank filed a case against you while you are in Qatar;then, you will not be able to obtain visa and exit the country without settling your debts.

The best way is to talk to the law firm that your credit card company is liasing with and they will be able to transact and negotiate with you regarding your debts. If you have no means to settle it. You may want to wait for sometime till you have the means to settle it and that's the only time you can come here.

All the best,
Ollie