Recent observations of GN-z11 with JWST have revealed a Ly alpha emission line with an equivalent width (EW) of 18 +/- 2 angstrom. At z = 10.6, this galaxy is expected to lie in the heart of reionization. We use a series of inhomogeneous reionization simulations to derive the distribution of the Ly alpha EW after traveling through the neutral intergalactic medium with varying average neutral gas fraction, x (H I). We use these distributions to place an upper limit of x (H I) < 0.88 at z = 10.6 at 95% confidence level. We compare our upper limit to different reionization history models, which include the recently identified enhancement at the bright end of the luminosity function at z > 8. We find that models in which faint galaxies have a higher escape fraction compared to bright galaxies are favored by the new data.