Did the person that gave you the gift card buy it directly from WN or did they buy it at another retailer like Kroger? If the person bought it at a retailer like Kroger and you have the activation receipt that came with it, I would take it to the retailer and see if they will exchange it. I had an Itunes card given to me once and the security code was unreadable and it was purchased at best buy and they were able to exchange the card out for a new one.
If the purchase was made from southwest direct and was recent I would have the person that bought it for you contest the charge with the credit card company.
If you go with the option of returning the card I would recomend holding on to the original card and mailing them a copy of the card or at least mailing the card with a method where you have proof they received it.
One other thing I would recomend if they don't solve the problem is file a complaint with the BBB. I had some problems with Northwest over an issue a couple years ago they would refvuse to help me out on. I filed a complaint with the BBB and the attorney generals office and as soon as they were contacted they worked with me. Companies don't want their businesses showing an unresolved compalint with the BBB.