What is the "code" - javascript, php, something else? Is it run by the user, or automatically?
If you are asking for the user to be able to click a button or such after the course is completed, you could do this using restrictions on a URL activity so that it isn't made available until after your course is completed (either by adding all the same activity conditions that compete your course, or by using a restriction plugin to hook off the course completion (https://moodle.org/plugins/availability_coursecompleted). The user could then click the activity to go to the url that executes the code.
If you are asking for a hook that runs on a course completion event (in the background, without user interaction), I have a plugin that observes a few typical course events https://github.com/frumbert/nosey_notifications which posts the event data to an external URL that you can then use in your own custom way.
There's also the Event Trigger plugin which sounds similar to Tim's plugin.