Row Column Matrix Problem with Flyback Diodes
This multiplexing works only with unidirectional current loads (ie led-s ). Otherwise the current will  go from high on one column to high to all other rows not pulled down then backwards through the coils to high on all other columns, not 24v since the current passes through two coils but enough to make trouble. 

Try this setup:







simulate this circuit &ndash; Schematic created using CircuitLab

Edit for more details:

This is the way the current goes through the matrix when a row and a column are selected:



Current goes to the left through LED and to the right through the flyback diode. The selected diode/coil will have full voltage, all other led/coils connected to the selected row and column will have almost half voltage. Putting a diode in series with each group led/coil + flyback diode will break the current path through non selected LEDs/coils.