Is it possible to make a reactor core in a capital ship and when you destroy it the whole ship will blow up like in Elite squadron?

Yes, but it will require some lua coding.

Does anyone know what the code it?

There is no prewritten code for it. You can look in the space luas (BF2Modtools/space_template/Common/scripts/@#$) for a model of some KillObject code.

or in the mygeeto campaign lua, i think you diasabeled a shield by destroying a generator there.

you could always use the linked destroyables function found in most any space map.

It would also involve adding an explosion to the various objects that constitute the hull of the capitol ship. Otherwise the objects would simply disappear, which would be rather anticlimactic. Also, it's advisable to activate a death or damage region for people not in a ship that covers the entire living area of the cap ship. Otherwise, I'm guessing that you would just start falling if you were on board when it happened. This is a lot of educated guesswork on my part, as I've never seen this done in BFII before, but that's how I'd go about it.