Aside from the question whether the coupling and connections would fit onto the subframe, engine, etc I'm not sure there's much point in doing this.
The K20A has a completely different torque/power band to the K24 and as such different ratios. I would imagine the K24 gears are taller to support the larger torque and lower rev limit. Putting a box from the K20A in there would just mean that you're shifting way more often and leaving the torque band quickly. I know some guys in the States have transplanted a K24 into a Civic but they also took the gearbox with them.