How to find load impedance when input impedance and reflection coefficient over range of frequencies is known
No, there is no way to determine two numbers, ( magnitude, phase) , from one data point.
However, perhaps you know more :  if you know the physical nature of the load, you can model it as a circuit. You can find values of the circuit that give you the same reflection coefficient magnitude as your data. Then you can calculate the phase of the reflection coefficient ( or load impedance) of your circuit model.
Of course, there is not only one circuit that leads to a particular magnitude response. However, lots of times you can see that, for example, this trace is acting as an inductor, this structure is creating some capacitive coupling, and so on.  You likely should start with a ladder type structure, as this topology is familiar to most engineers. I would start with a lossless ladder terminated in a single resistor. Then you find the values of the inductors, capacitors, and resistor that match your magnitude data, and from that you can find the phase.
Off the top of my head, you have some kind of band pass network at 68Mhz terminated in either 17 ohms or 150 ohms. Start from there and go to it with some nice computer program.