You're talking about the application's interface. You'll want to react to the dropdown's event that fires when you change the selection, which will vary depending on what environment you're using. If you're using asp.net, it's the SelectedIndexChanged event.

When this event fires, you'll want to query the value from the database for the code selected and then display it below your dropdown. You can do this with an SQL function, an SQL stored procedure, by caching the table of codes and descriptions on the web server and then selecting the value from there, or a host of other approaches.