By default, Poedit does not have the ability to parse Twig templates. In Twig documenation there is a simple example which shows how to extract translations. This can work with few modifications, but I wanted to make reusable tool which will allow you to parse Twig templates just like you do with plain PHP templates.
Twig Gettext Extractor can be easily installed through composer or cloned from GitHub. Once you install all dependencies you can setup Poedit by adding new Twig parser (described in README).
After that you can use Poedit to parse your Twig templates (Catalog > Update from sources). No special catalog settings required, it will work with default keywords.
Feel free to use it, give feedback, contribute, report issues…