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Say I have written code that performs a physics calculation. After this, I get a paper published based on the results of the code. In the interest of advancing the progress of science, I upload the code used for the paper on, say, GitHub. I also post a link to my code on GitHub on my website. I do this to facilitate discovery and use of the code by those who are interested in my results. Imagine that someone, in the process of reproducing my results (using the aforementioned code), discovers a flaw in the logic of the code. Correction of this logic flaw leads to invalidation of the central idea of the paper.

Will this lead to retraction?

Will there be any positive gain to me as a result of publishing of the code?

If the main idea in the paper has been invalidated by the correction in the code, you would do well to try to retract the paper yourself. This is just a point of professional ethics. It also protects you in a way from future claims if people don't examine everything thoroughly.

The journal may not be able to actually retract the paper, but might be able to post a note (printed or online) that the paper has a flaw (noted by the author, hopefully).

But others, relying on the original thesis of the paper might be misled in their own work. You really don't want that to happen.

Honesty in science is assumed. Make it so.

You might also be able to publish a better paper, based on the corrected code. Work toward that end.

Will there be any positive gain thanks to the publishing of the code to me?

Publishing the code is necessary to make the calculation reproducible and the results verifiable. If I were the referee of your paper I would likely insist that you publish the code. So the “positive gain” would be that your paper will not be rejected outright. It will also help your reputation and build up other researchers’ impression of you as a serious, careful scientist who understands what it means to do good science.

Besides, what you are asking is essentially “is there a positive gain to behaving honestly”. I’m not going to enter a philosophical discussion about honesty and its benefits here, but just think for a second about what you’re saying. Even in a specific context of academic research, your question can be rephrased as “I am thinking of hiding information about the way I did my research that would be essential for other researchers to verify my results. Is there a positive gain from not hiding this information?” Again, think about what you’re asking.

It’s clear from the question that you are in fact a person who is motivated by a desire to advance science and wants to do the right thing. That’s great, and the conclusion is that it is your duty to disclose the relevant information about your research that would enable other researchers to check your results. If the results later turn out to be invalid, then you and the journal you published in would need to deal with it in an appropriate and responsible way, either by issuing a note pointing out the error, or (which typically would happen only in really extreme, egregious circumstances) by retracting the article. Honestly I don’t think this is something to worry about too much. As long as you’re acting in good faith and doing your best to do good science, you are adding to the sum total of human knowledge and your work has value. That’s what matters, and that’s what you will ultimately be judged on by your peers in the community.

@Buffy is certainly right that Science itself gains a lot if people publish their code. Papers without code (the norm in many scientific areas) are hard to reproduce or build upon.

But you ask what you gain from this, or if it might harm your career.

First of all, it is unlikely that somebody finds a major flaw in your program and it is even more unlikely that a journal will retract the paper because somebody else (not you) requested this. Most of the wrong or doubtful results just stay in the literature.

What is much more likely: Somebody will actually use or extend your results, and help you improve them. So he/she will cite you or work with you on a future paper. This is definitely something you want.