I’m thinking about integrating the new awesome WordPress block editor (Gutenberg) outside of its environment (WordPress core), so is there any way to get just the text editor code and use it for example in another CMS or framework or just a simple HTML page?

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Yes, You can use Gutenberg as a standalone app or CMS agnostic app. Drupal using Gutenberg as a npm module and then integrating in their own CMS. Drupal Gutenberg is decoupling Gutenberg from WordPress and using as JS editor Gutenberg JS. This way, developers can build block for Gutenberg and port it to two different CMS.