You can certainly write to the authors to ask for the code even if the paper is not yet formally published. While the chance of them sharing it might be more if it is formally published, I don't think it is rude to ask. You could perhaps include some context on why you are interested, if you do so.
Nevertheless, to find out where a paper has been published (if any), you could try the following:
- Search Google / Google Scholar.
- Check the "Comments" metadata in the arXiv submission. The final publication venue is often mentioned there.
- Check the websites, Google Scholar profiles, DBLP profiles, etc. of the authors.
- Check with your university library.
You could check the databases of individual conferences, journals, or societies as well, but these would almost certainly also show up on a Google search.
For your broader goal of finding the code, a few suggestions, before contacting the authors:
- Check the paper thoroughly, look for any links in the text, particularly in the introduction or experimental sections, and in the footnotes.
- Search Google, GitHub, and similar resources. Sometimes there are third-party implementations available, in case that is helpful to you. If the authors have given a name to their technique / tool, searching by this name, in addition to the paper title, can help.
- In certain fields, there may be specific resources available. For example, in machine learning, paperswithcode.com maintains a database of papers along with code by authors and third-party implementations. For several popular tasks, it also maintains leaderboards of methods and their associated paper and code.
- Check the authors' web pages and their labs' web pages. A link to the code might be available in the publication list.
- Check for implementations in future papers that cite this paper (unless the paper you are looking at is very new). Others may have compared their methods with that of the paper, and may have an implementation included in their own code. Survey papers are also a good place to look.