ACR CAPT REPORTS OVERLOOKING A NOTAM PERTINENT TO THEIR LEGAL RELEASE TO ZZZ XXR CATII WHICH IS NA.

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WE WERE DISPATCHED TO ZZZ WITH WX BELOW CAT1 MINIMUMS AND A GOOD ALTERNATE WITH GOOD WX. WE WERE RELEASED WITH A REMARK OF 'RELEASE BASED ON CAT 2 WX MINIMUMS.' MY FO AND I SPENT SOME TIME LOOKING AT THE WX AND THE ZZZ XXR CAT 2 APPROACH PLATE AND CALLED DISPATCH TO CLARIFY WE WERE ALL IN ACCORDANCE WITH THE LEGALITY OF THE RELEASE. WE ADDED AN ADDITIONAL 2000 LBS OF FUEL FOR POSSIBLE HOLDING. AFTER DEPARTURE WE SENT FOR AN ATIS AND NOTICED THAT ZZZ XXR CAT 2 WAS NA. WE CONFIRMED THIS WITH THE NOTAMS IN THE WX PACKET AND REALIZED OUR MISTAKE. THE SAME ATIS SHOWED THE WX TO BE ABOVE CAT 1 MINIMUMS SO WE CONTINUED AND LANDED AT ZZZ WITHOUT ANY PROBLEMS CAT 1. THIS WAS COMPLETELY UNINTENTIONAL AND MY FO AND I HAVE TALKED ABOUT WHAT WE NEED TO DO IN THE FUTURE. WE AS PILOTS NEED TO BE MORE DETAIL ORIENTED IN THE PLANNING PROCESS AND WE NEED TO SPEND MORE TIME IN THE NOTAMS TO ASSURE WE ARE IN COMPLIANCE. IF THERE WAS A WAY WE COULD HAVE A COMPUTER PROGRAM THAT WOULD RED FLAG CERTAIN NOTAMS WHEN THEY CONTAIN THE SAME WORDS THAT THE RELEASE REMARKS SECTION CONTAINS THAT MIGHT BE BENEFICIAL. WE ARE TASKED WITH A LOT OF INFORMATION TO LOOK AT IN A SOMETIMES LIMITED AMOUNT OF TIME. I TAKE FULL RESPONSIBILITY AND WILL IMPROVE IN THIS AREA. I DO THINK THAT ANY NEW PROCEDURES AT THE COMPANY THAT ADD TO THE PILOT'S WORKLOAD AT THE GATE OR DURING THE PREFLIGHT PLANNING SHOULD BE LOOKED AT VERY CAREFULLY WITH RESPECT TO THE AMOUNT OF DISTRACTION THAT IT WILL CAUSE.