Ah. First go into "option" then "gameply" then klick on "show all ship designs".
After that save it and go into the designer. Launch the designer, klick "new design" Then you will see all the different design choices. Tiny, small and so on. But the important part is this: When you look down in the middle you see a small "gear" symbol. Klick on it. Here you klick on "show parts from other styles" and "Show design gizmos".
The important part is "show parts from other styles" but the design gizmos helps you to design ships faster. You can basically adjust parts of the ship in the designer itself. It is sometimes easier then doing it over the overlay in the right corner. But you still can use the overlay.
After klicking the two buttons you will get all the available parts of all ships in the game. It can be at first overwhelming but you will get used to is very fast. By the way you can enable "Show starbases" in the normal option menu. But i have disabled it right now. Because the starbases are bugged right now, when you design them for other people. When you upload starbases, people can not see them after downloading. They are invisible in the designer.
When you want to design this ship, it is important to use the "offset" option a lot in the right corner ui to move parts into each other. Furthermore when you look at the first tab of the ui "scaling" you can disable the proportional scaling for the part you are using right now by klickng on the small button down in the corner called "proportional scaling" then you can adjust all the parts the way you want. A lot of parts then can be changed to completely different forms. Even completely new looking part designs.