Continous liquid level measurement loop connection device
Motors are electrically noisy.

One possibility is that the electrical noise from the motor is being conducted to the 4-20 mA device of the power line, corrupting its signals.  That's frankly the fault of the power supply in the 4-20 mA device, indicating crappy design.  There is really no excuse for that since proper line-connected power supply design already assumes the line is noisy.

It would be interesting to know know which tank level guaging system you are using.  Is it a pressure cell, ultrasound, radar, level-sensing "tape", something else?  What manufacturer?  I have some familiarity with this business and might be able to provide more insight.

Another but more remote possibility is that the 4-20 mA device is getting corrupted from noise radiated by the motor.  There is still no excuse for that either.  Proper design of sensitive analog electronics includes minimizing susceptibility to external radiation.  There are limits of course.  You can't really expect proper operation when you're 10 feet in the air 100 feet from a multi-killowatt radio transmitter.  If radiated interference is the problem, then just separating the motor and 4-20 mA device will help.  Radiation power density descreases with the square of the distance from the transmitter.

Of course this is all assuming that the 120 VAC outlet can supply enough power to run the motor and anything else connected to it.  Measure the voltage with the motor on and off.  If the voltage goes below 100 V, then that's the problem.  In that case, the 4-20 mA device is not at fault since you're feeding it power out of (the assumed) spec.