I think at Zaliv shipyard they have that. Zaliv shipyard has the biggest dry docks in Russia. It used to be in Ukraine. Anyway, Russia won't build large carriers, only helicopter carriers.
Actually, I think the real mega shipbuilding base for Russia is in Bolshoy Kamen, which is right next to Vladivostok. Look at below:
The Red Box on the upper right corner is a huge floating submersible dry dock (size approximately 280m by 65m)
The Yellow box on the lower left corner looks to be a gigantic dry dock in the making. Measuring the shadows, it seems like it is 110m wide and at least 500 meters long. This, to me, looks more like a place where it would be easy for the Russians to build a large or heavy aircraft carriers.
Google map position: