During the arraignment they probably ask you "do you waive time" and you said yes. without that they wouldn't have gone beyond the limit. Think back to the arraignment date.
Didi you wiave time? This would have required a time waiver. If not then it is possible to make a motion to dismiss on this ground.
The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case.