How to pass exitCode from Katalon to Jenkins in order to inform of Test Case failures

You mean the report prodcued by the Basic Report plugin of Katalon Studio?

Jenkins knows nothing about it. Jenkins has nothing to do with the Katalon’s Basic Report.

So I would reword your question as such:

Well, possibly there is something wrong in your test project. You need to fix it before getting the Basic Report.

What’s wrong? — I do not know, as you have provided no information. If you want somebody to help you, please have a look at the following post:

Your question would be “off topic” from the point of view of this old thread.
If you want to ask question, please make a new post and provide information (log, HTML, page screenshot, test case script etc)