As John said sawn lumber won't work. You could build a floor for storage only with I - joists and plywood deck. If headroom, build it below the roof/wall connection, depends on garage door opener hardware.
Here is info, notice the on center chart below for different spacing (cheaper):
http://www.ilevel.com/literature/TJ-4000.pdf
Be safe, G
Here is info, notice the on center chart below for different spacing (cheaper):
http://www.ilevel.com/literature/TJ-4000.pdf
Be safe, G