Jobless between 17th Feb to 27th March. No Health Insurance from 17thFeb to 31stMay.Due to employer's mistake. Can i exempt from NJ state health tax penalty?

Lost job on 17th Feb 2024. Got new Job on 27th Mar. Due to employer's software issue could not be able to get the health insurance until 31st May instead of 27th Mar. So in total i was without the Health insurance from 17th Feb to 31st May. (i.e. 3 months and 11 days) Can i file the exemption from NJ state penalty for not having health insurance during this period as it was not the mistake of mine? But it was due to job loss and Employer's mistake. If yes then how? Also I have already filed the taxes so should i file the amendment?