Severance offer, what should I ask for? (update)

I was offered 4 weeks of severance after 4 years as a software tester, and I have a few days to sign. I do not usually post, so bear with me. I do not want to leave money on the table. Did anyone negotiate and succeed?

Thanks for writing this out. I went through something close to it 10 months ago, and it got easier once I kept a simple log of every call and form.