How to create a recovery disk after using the up-to-date program? I used the Up-to-Date program to update OSX to Mountain Lion.

Now I'd like to create a recovery disk, but I can't use the same code to redeem installation package, and from the Apple Store it seems that I don't own a copy of Mountain Lion and that I should buy it to be able to download it. How to get the InstallESD.dmg file?

Or how should I create a recovery disk without this file?
Apple's Recovery Disk Assistant
...enables you to create a recovery USB. While this recovery USB does not contain the installer image, it is able to install Mountain Lion (see 3rd paragraph).
You can download the official software from Apple here. Note that you can create the recovery USB only if you have a Recovery HD partition on your Mac. You can verify this in the Terminal using: diskutil list.
The Recovery Disk Assistant requires just 1GB because is does not store an OS X installer image (usually named InstallESD.dmg). Instead it will download the latest version of Mountain Lion right before the installation - if the recovery USB has been created in Mountain Lion.
You are still able to use the recovery USB without internet access if you just want to open Disk Utility from it for example.