How to "hold" TTL pulse
You can use PWM to genrate any kind of staircase or hold signal you want to generate. The output of the signal as such should be buffered.    

Second method is to use multiple transitors, to generate multiple voltage Levels. I hope you have spare digital output pins on Arduino.    

Below image depicts the basic idea.


Q3, R3 and R6 aren't required. You can pull up R4 to 2.3V. Use voltage divider rule to calculate value of R5, so that 1.3 volt is generated. Here you have the waveform shape you need.  

Specify, more about solenoid and I will edit my answer as needed.  

Edit:
I would suggest to follow Tony Stewart answer as it is from the same solenoid manufacturer.