I've read the edited version of the question, and if I understand you correctly, you want to run a program from SSH without showing you the GUI... you just want to run the program and it depends on X Windows, so you need it to connect somehow to X Windows on the server itself.
There are two things you need to do. You need to allow connections from outside of X Windows, and then you need to tell the shell (in SSH) which X server to bind to.
First, allow incoming connections to the X server. Open up a terminal window in X Windows on the server machine. (You must have access to that, otherwise you cannot do this.)
Issue the following command:
It should tell you "connections allowed from all hosts" or something to that effect.
Then, while still remaining in X Windows, issue:
This will tell you the display ID. Write it down or remember it. Typically it will be ":0" or ":0.0" but don't worry if it's different.
That's all you need to do from within X Windows itself.
Now SSH into the server from wherever you want. Issue the command:
And that should be it! Now you should be able to run any X windows from that SSH shell, and it will pop up on the local X Windows server.
Hope it helps!