Where does the error occur? After you launch Bannerbomb? If so, check if you are on v2, and reinstall Bannerbomb. Then try again. The error can occur most likely because of a faulty Bannerbomb.
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The error code you received indicates the system is attempting to load unauthorized software. Unauthorized modifications to save data or program files may impair game play or the Wii console and should be removed.
Nintedo Error 004
This error is displayed when you try to load an invalid banner, e.g. Bannerbomb." According to Wiibrew.