We evaluate the limiting imaging sensitivity of a two-dimensional faint phase object, placed within an interferometer. We consider the case when both input ports of the interferometer are illuminated by spatially multimode quadrature-squeezed light, and a differenced detection scheme where spatial resolution is used. This provides the Heisenberg-limited measurement sensitivity of the spatial phase distribution in the object. The optimum choice of space-time scales of the system and the resolving power of the measurement in space and time are discussed.