There's a bit more to it than 2x2.
Each base technology has at least one blueprint that enhances it. You can also (in addition to the blueprints) install 3 upgrade modules. For example, the boltcaster has the "Barrel Ioniser" tech, which you can install in addition to the three upgrade modules you have. Similarly, the mining beam has the "optical drill" and "advanced mining laser" blueprints, and you can have 3 upgrades in addition to those.
Modules with numbers on (and base weapons) gain a "synergy" bonus for each related technology they touch (groups shown by the coloured borders) - so you want your best modules to have as many related modules as possible touching them. Some modules don't have a value on, for example ones that enable functionality, so they give synergy bonuses but don't gain them - these can be places to fill edges / corners.