I know some parts of the world require notice by law, so I'm sorry if you can't do this.
If you're starting a new job in a few weeks, rather than give 2 weeks' notice and working your arse off doing transition memos for your old company, take PTO or sick leave if you have it or it is available to you. Do something for yourself/your family, or handle those personal items you haven't had time to handle because you've been working for so long. Remember, your new life is your own and you've given more than your fair share to the company. Use the time between accepting a new job offer and starting a new job to do what's best for you; not your now-former employer who is likely already mad at you.