[Fyron]

I just want a regular Shipyard facility but with a diferent graphic that its only avaliable for the Homeworld as an starting facility. Is that possible?

Yes. Copy the Space Yard III facility, and place it right after the original SY III. Make the new one slightly more productive (or however you want to do it) and make it cost as much as Cultural Centers. Actually, doing this will probably cause the AIs to try to build them on colonies. Maybe you should try experimenting with placing it before the other SYs, try different family numbers, etc., to try to get the AIs to not build them on colonies.