> How can I configure some "Run script" (typically a "make check" launched from
> eclipse), to test and debug my code ?

I just remembered this:
You can use the "External tools" in Eclipse in "Run > External Tools >
Open External Tools Dialog...". Here, you can create a program launch
configuration, define what executable to launch ("make"), in which
directory to start it ("${project_loc}"), and give it "check" as
argument to follow your example. You can also add it as a favorite to
access it faster.

Then, you will be able to start it by clicking on the "External tools"
button on the tools bar.