I began typing a response but after some thought, I realize that the answer to your dilemma is complicated by the fact that you may seek 2 positive outcomes rather than 1 for your problem. Here's a potential solution:

"Work-Productive" Saturday

computer/coding related and results in a viable product

+ full-time involvement by other participating individuals

= hackathon/co-founder meetup for projects (perhaps non-profit ones would circumvent IP/competitive issues?)

"Personal-Productive" Sunday

not drinking/pub related

+ can result in friendships/relationships

= any activity that you truly enjoy/want to try out that is NOT computer-related and NOT solitary by default (e.g. going to the gym to lift weights, while is a great activity, may not be recommended for this purpose because it's hard to chat people up when they are concentrating on their new max reps. Whereas a team sport that requires communication may be more amenable.)