Will Selling your colony (My Ship) Get rid of the gravship?

So I was casually raiding an enemy base when I got the Archonexus quest, which essentially lets you sell your colony for an archonexus piece, one of three you need to find the location of the archonexus. I am familiar with this. But this time, I am doing the new gravship scenario, and the colony is the gravship. I am wondering if selling my "colony" will sell my gravship as well, or if it will stay with me. Any ideas?

https://preview.redd.it/6kxorny6eedf1.png?width=616&format=png&auto=webp&s=4f99837de5ab8971b6ddffefe45b1a696fb68176