A current converter need power supply to work. As long your power supply is limited to 3V ( assuming there is no voltage lost on the FET), the voltage swing on the load could be 3V so the maximum load value could be be R = U/I, 3V/20mA = 150 ohm. Such load swing could be to small for a long wire (with a large voltage drop). The minimal load resistor required by astandardised 4-20mA loop is around 1k (22V-24V supply)
Start your design knowing the wire lenght and estimate the resistance first.
Then define the driving voltage value, voltage sign and reference point (ground or V+ or V-). After that you could imagine how looks the current converter ( a simple current mirror, a voltage to current using an operational amplifier, etc).