To each input of the keypad connect a fixed resistor - a different known value with significant difference in resistance for each input. and connect them all in parallel to a digital output pin on arduino
Wire 4 of the row or column pins to 5v supply directly and the rest 4 in parallel to an analog input and measure voltage / compare it to preset values.
I think it would be better than a regular keypad in terms of response rate as the scanning is limited to a single pin and then lookups.
The resistor approach would not work even if noise would not be present.
The standard approach is to go for shift registers.