The rows have a common gnd ant the columns have a common anode.
So TBA20-12?
The resistors are on the anode pins?
What is frequently done is to drive all the anodes for row1, then take the cathode for row1 low.
turn off cathode1, change the anodes for row 2, turn on cathode2.
The cathodes would have to sink 7 x 20mA each, so a part like ULN2003/ULN2803 would be used to buffer the arduino pins driving those signals.