Hey, I've purchased xbox gamepass live, but I am not able to play Call of Duty online with...

Oh OK so if I am right that I should be able to play GTA and Call of Duty online on the Xbox 360?

What Game Pass did you purchase? There's not one called Game Pass Live. If you bought standard Game Pass for console, it does not include Gold so you wouldn't be able to play online. You would need Gold or Game Pass Ultimate.

My name is Fernando I'm an independent consultant, I'm happy to help.

What device are you experiencing this issue on? And just in a specific game? Is there any error code or message? Let me know so I can help.

Hello dear Gamer, first it's a pleasure to be able to help you today.

My name is Vinicius.

I am a gamer and independent advisor on the XBOX community platform.

Hey A1DYN101, how are you today? Hope you're well.

Call of duty black ops 4 has a good zombies mode and it has 4 player split screen.

Other games worth playing (All have 4 player split screen but don't have zombies)

Halo master chief collection (Gamepass)

Rocket league (Gamepass)

Overcooked 2 (Gamepass)

Riptide GP (Gamepass)

Perfect Dark (Gamepass)

Borderlands Handsome collection (Gamepass)

Worms W.M.D (Gamepass)

Gears 5 (2 player, Gamepass)

State of Decay 2 is also a good one, but unfortunately, doesn't allow split-screen, only online co-op. :/

Only some games have support for playing on one console in Online Multiplayer. Some parts of Call of Duty, for example, have such support for playing.
For clarification, the main service is Xbox Live Gold. And the Xbox Game Pass is another Xbox service and you can play free games if you have a Gamepass membership.