After getting the suggestion that maybe the other characters don't want to have to be apart of the situation (thanks KY25), I decided to play through the whole game (and remembered to save when I got super far) and managed to complete both the research table and upgrade station, as well as getting the radio tower and beating that part. I then wanted to figure out the code, because I now knew it but still didn't know where to put it. I figured maybe the controls menu because it has the same amount of letters as the code, but it didn't work. I might be completely off track, because the only hint I know of that tells you were you might be able to put the code in was talking about the menu. I'm not sure if that was changed by the time I'm playing this, or if I'm just blind. I am currently in the caves right now, trying to figure out whether or not it has at least a hint on where you can use the code, but keep getting demolished by the slimes which keep destroying my elevators and wind turbines.
I can now confidently say, my original opinion of the game was invalid, and I am now in love with this game, not counting the few flaws I've found with the game.