I should update this thread with new details since some of it has changed.
The aircraft was a 737-201 Advanced, which means that it has been modernised from a -200 model, likely before the Classic series was being delivered. The registration was XA-UHZ
The 737-201 was 39 years old and was being operated by Global Air for Cubana, as such the crew was Mexican. Prior to being sold to Global Air, the 737-200 was used by the US Navy for 5 years. It was initially delivered to Piedmont Airlines, and then was owned by a leasing company after Piedmont stopped existing.
The 737s were being wet leased because Cubana's own An-148s were grounded for issues relating to landing gear (my parents were in Cuba 2 months ago and were due to fly on the exact same route this incident took place, the An-148 did not take off due to a landing gear fault, and passengers were taken to their destination by bus instead).
Cuban media reported initially that a 737-500 operated by Blue Panorama had crashed, which initially caused confusion.