I ran a 60 amp sub into my garage a year ago. The run was also about 60' away from the 200 amp main, and I used #4 THNN. Using a chart located on the Internet, it appears you will need to go to a #2 or #3 THNN.
The following capacities are for copper conductors with THWN, THW or XHHW insulation:
Individual conductor ampacities - 75C temperature rating
#10 - 30 amps
#8 - 50 amps
#6 - 65 amps (can be protected at 70 amps)
#4 - 85 amps (can be protected at 90 amps for outbuildings. If this sub-panel is in a dwelling #4 may be good for 100 amps - see notes below)
#3 - 100 amps
Please see the notes at the end regarding wire ampacities and temperatures!
Number of conductors needed
For various reasons, it is best to run 4 conductors. This would be two 'hots', one grounded conductor (neutral) and one equipment ground (bare or green).
Remember, usually it is best to have a qualified electrician come out and give you on scene advice.