Who do I ask for a reference after a layoff? after 13 years as a web developer

My manager was laid off too and I am unsure who to use as a reference. A colleague offered to vouch for me. How do you ask politely?

Ask former colleagues and supervisors in a short message and give them a summary of the job you are applying for.

I kept a note of my results so my references could be specific. They appreciated it.