Normally it runs out of the box... You seem to have something strange on your system...
That's what I read and hoped.
Can you make a screenshot of the compiler settings for gcc (Settings->Compiler->Global compiler settings->Select: "GNU GCC compiler" from the dropdown->Toolchain executable)?
See the attachments.
Can you try to generate a new project? After you have started codeblocks the first time?
CB is running for years now on my system. (Usually w/ avr-gcc.) The gcc project is brand new.
Please restart codeblocks after changing the settings and try to create a new project, do not use the old project.
I restarted after autodetect and a few moments ago started once more - no change. CB doesn't find gcc.
Few minutes ago, I generated a new test project and started gcc on the generated main.c - same effect, same error diagnostic.
Well you did not give any information if you have installed any compiler, or if yes, what compiler do you have installed. So my first advise is to install a compiler...
See my posting from 02:43:54 pm. On most linux systems and specially on debian like systems, gcc is preinstalled. Linux Mint is such a system. And for sure the compiler works, I frequently use it to compile new packages from source downloads.
If you have installed a compiler then say so and also give version and installation method...
See my posting from 02:43:54 pm - there is the complete version info of the compiler.