We construct the supergravity solution in 11 dimensions describing D6-branes wrapped around a Kähler four-cycle with a B-field along the flat directions of the brane. The configuration is dual to an N = 2 non-commutative gauge theory in 2 + 1 dimensions. We also construct the four associated independent Killing spinors. The phenomenon of supersymmetry without supersymmetry appears naturally when compactifying to type-IIA or 8d gauged supergravity. Therefore, this solution also provides an lid background with four supercharges and four-form flux, which is not obtainable from 8d gauged supergravity.