You can do this in Joomla quite easily, but actually managing the codes may be a little time consuming.
If you were to post each "code" as an article in joomla, then you could set each article to stop publishing on a certain date, which would unpublish it on that date. That should have the required effect.
With regards to actual design, I don't know of any free templates off the top of my head, but I'd suggest hunting around for one that meets your style requirements. Or, if you have any budget at all, you could opt for a commercial template.
One last suggestion though - I'd recommend looking at the K2 component for managing your articles. You can associate an image with each one, and use it in modules as a link to that article (similar to how the boxes beneath the This month's featured retailers: heading are on the front page of that site).
Alternatively, YooTheme's Zoo component ( http://zoo.yootheme.com
) is another useful content creation component.
Both of those will allow you to better control your articles.
Hope this helps.