Is "Cod Mod 2" a Real Game on Wii?

No game titled "Cod Mod 2" exists on Wii (or any platform). You are likely misremembering one of the following:

Most Likely Confusions

• Call of Duty: Modern Warfare 2 (2009) – Released on Wii as Call of Duty: Modern Warfare – Reflex Edition (2010, Treyarch port). It is a full campaign + multiplayer (no DLC).
• Call of Duty: Modern Warfare 2 (2022) – Current gen only (PS4/PS5, Xbox One/Series, PC). Not on Wii.
• Call of Duty: Black Ops (2010) – On Wii (full MP, no DLC).
• Call of Duty: World at War (2008) – On Wii (MP + Zombies).
• Call of Duty 4: Modern Warfare (2007) – Not on Wii. Only PS3/360/PC.

"Mod" Confusion

• PC Mods: CoD4 and MW2 (2009) have massive mod communities on PC (e.g., MW2 Remastered Mod, IW4x, SM2). Wii cannot run user mods (no homebrew loader for CoD titles easily).
• Wii Homebrew: You can run Gecko OS / Riivolution patches for texture hacks or code patches (infinite ammo, etc.), but not "Mod 2" as a standalone game.

If You're Looking for a Specific Mod

Describe the gameplay: zombies? tactical? campaign remake? multiplayer overhaul? That will identify the actual project (likely on PC).