Hi Nikola,
thank you for getting in touch. Basically you are doing everything pretty ok, however you are missing 1 thing. Generally whenever you create a grid gallery portfolio item you need to upload the images to be attached to the portfolio post. Featured image will be used only for the ‘Image’ as a main image, however for the grid you need to upload rest of the items.
So here is how the steps would look like:

1. Select Gallery Tab
2. Add new
3. Input normal content and title
4. Set Portfolio option to Grid Gallery
5. Add Image to Feature Image
6. Upload images to the grid gallery post via ‘Add Media’ (please note the images need to be uploaded so they will be attached to the post and processed by the script).
7. Save changes

Then you portfolio grid gallery item will show up as a grid.
In case you want to add the filterable gallery page (main gallery view) you need to create page and select 2,3,4-folio columns from the page template. Then create a menu item pointing to this page. Then, you will have a page with filterable view. And of course then you can add more post to the portfolio via Portfolio ► Add New.
Please let us know whether that helped.
Best regards,
Jake