Laws vary from state to state. Yes, driving 20+ miles over the limit can be considered reckless. If you received the ticket, it should state what it's for and a fine should be listed. If it's for reckless driving, go to court and plead your case for a lesser charge.
Is it for speeding? Considering you know you were speeding and a radar would have been used, if you go to court, your chances of being found not guilty are very minimal. I would just pay the fine and be done with it.
Are you concerned about it being on your record for insurance purposes? Taking a driving safety course, could help to reduce your rates.