To use the codes with Dolphin choose "Dolphin INI" as file format instead of "GCT" to download the codes formatted for use with Dolphin. Then right click the game in Dolphin and click on "Properties" and on the bottom left corner of the property window click the "Edit configuration" button. Close the property window. Open the text file you downloaded and copy everything following the "[Gecko]" tag below the same tag in the configuration you just opened. If there is no "[Gecko]" tag (it should be the first tag), create one on top of your configuration file. Save and close the configuration file.
Reopen the property window, select the "Gecko-Codes" tab and check all the codes you want to be active. Most (but not all codes) will work with Dolphin. However, Dolphin has a code limit which is reached rather quickly. So if your game crashes right after it starts, you probably have too many codes active simultaneously.