This widget code previously provided is no longer available through Disqus, though widgets can be recreated using our API. The Popular Threads widget can be recreated using our threads/listPopular method.
While there currently aren't any official examples, the flow of the widget will look something like this:
Pull results from the threads/listPopular endpoint.
Save them locally to a database.
Pull these results from your local database and display them on your website.
Periodically update the results via cron or other script.