If more than 2 switches may be closed at a time, the you'll need to connect a diode (1N4148 or similar) in series with each switch, otherwise you won't be able to determine exactly which ones are closed.
A 10x12 matrix would use one less pin than a 7x16 matrix.
As an alternative to using a Mega, if you will be connecting diodes in series with the switches, then you could use a 74HC4515 demultiplexer to generate 16 column lines from 4 pins. Then you can read a 7x16 matrix using just 11 Arduino pins (i.e. 4 for the column outputs and 7 for the row inputs).