Multiple pushbutton read simulatenously
20 inputs needs 20 pins. 5 x 4 matrix requires 9 but for simultaneous button press reading you will require a diode on each button to prevent backfeeds from the column being scanned to any of the others.



Figure 1. Problems with scanning keyboards with simultaneous multiple keypresses. In the example column C1 is being scanned and since only S1 is pressed the expected result is that row R0 only should return a 'pressed' signal via S1. If S2 and S7 are pressed as well a backfeed occurs onto C2 and R1 will also return a 'pressed signal' indicating that S6 is pressed as well.



Figure 2. Addition of a diode on each key prevents the backfeed problem. Source.

Since it seems that you are going to require a micro to encode the information it seems a pity to add additional hardware for the keyboard.

You may find that your decision is determined by the available keyboard type.