[math-fun] Signed area puzzle

Every closed path on a square grid has a "signed area" equal to the sum of the winding numbers around the grid squares. What is the maximum possible signed area of a closed grid-path that lives in [0,8]x[0,8] and doesn't re-use any edges? I found one with signed area 114; is this best possible? An easy upper bound is 120 (the sum of the upper bounds on the individual winding numbers associated with the 64 grid squares). Jim Propp