We study the fractal structure of space-time of two-dimensional quantum gravity coupled to c=-2 conformal matter by means of computer simulations. We find that the intrinsic Hausdorff dimension d_H = 3.58 +/- 0.04. This result supports the conjecture d_H = -2 alpha_1/alpha_{-1}, where alpha_n is the gravitational dressing exponent of a spinless primary field of conformal weight (n+1,n+1), and it disfavours the alternative prediction d_H = 2/|gamma|. On the other hand <l^n> ~ r^{2n} for n>1 with good accuracy, i.e. the boundary length l has an anomalous dimension relative to the area of the surface.
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