Intel software not starting on Ubuntu Linux on M1 Mac

Hello
I have developed a software which always worked fine in Ubuntu Linux on Intel Mac. Now I have switched to M1 Mac with ARM processor.
I also have installed the latest Parallels Desktop V18.1.0 and on choosing Linux Ubuntu Parallels has installed "22.04 ARM64". This was all easy....
Now I have built my app on Mac for Linux with option "x86 64bit". When I then try to execute this application on the Linux side it says (translated):
./mytool Can't execute the binary file. Error in format of the program file.
So i assume Linux runs in ARM mode and won't execute Intel based software. This confuses me because Parallels says this is possible: https://www.parallels.com/blogs/parallels-desktop-m1/
I read it that way that I should be able to run AMD and Intel based software in Parallels on a M1 Mac.
I also have Windows 11 installed in Parallels and building my app with "x86 64bit" option it runs smooth on Windows (AMD).
Do I have to consider something special to make it running on Linux Ubuntu?
I also downloaded an intel versions of Ubuntu (in case this would solve the problem) but Parallels refuses to install it, translated: "The selected image can't be used because your Mac has an Apple processor of the M series which doesn't support Intel based OSs"