Its an artifact of your logic analyzer - the unused outputs are high impedance and will thus capacitive couple to each other via the wiring harness of the logic analyzer.
Connect the outputs to ground with 10k to 1k resistors and the behaviour will probably go away.
High impedance points in a circuit are very sensitive to noise like this, its why you never leave a logic input floating for example.
I also note you haven't used a decoupling capacitor or connected the COM pin to +12V, as it required when switching inductive loads.
Not the case at turn-off - you are probably thinking of turn-on when the dI/dt is limited, but at switch-off the dI/dt through the switching device is high (the current diverts extremely rapidly to the diode) and decoupling is needed just the same as for resistive loads.
Which relates to the common misconception that it is appropriate to attach the diode close to the inductor/ solenoid.
The current through the inductor does not change rapidly, but all the current promptly diverts from the switching device to the diode.
Since the switching device current derives from the power supply, this means the actual current transients occur in the supply line (and diode but not the inductor!) so it is important to minimise the size of the loop consisting of power supply bypass capacitor, switching device and diode; all must be kept in close proximity to suppress the propagation of switching transients.
