I would suggest you investigate different techniques - I do wonder even if you could measure down to 120ps that this would be a solution for you. Laser distance measuring devices use a technique called undersampling - it's a bit like using a strobe light on a moving object. This only works with repetitive signals as you need to synchronise your 'strobe light' with the signal. Another analogy is like looking at a high frequency signal on a digital oscilloscope at too low a sampling frequency. The net result is that your picosecond signal is warped down to microsecond level where the timer/counter in the micro can be used.

Maybe you need to look at strain gauges or maybe laser infereometry (I don't think I spelt that one right!!.