The continuing improvement of high-speed area-scan cameras has made possible the construction of parallel optical coherence tomography (OCT) systems that are competitive with the fastest demonstrated swept-source OCT systems. Unfortunately, when imaging through turbid media using a partially coherent source, parallel OCT suffers resolution loss from coherent multiple scattering, a phenomenon known as crosstalk. We demonstrate the use of a full-field OCT system employing multimode fiber in the illumination arm to reduce the spatial coherence of a partially coherent source. By reducing the spatial coherence area below the system's lateral resolution, we create a spatial coherence gate that rejects these multiply scattered photons. We quantify the image quality and resolution improvement of this method by comparing images of a USAF test chart acquired beneath turbid phantoms using both coherent and incoherent illumination and computing the resulting modulation transfer functions. We demonstrate the feasibility of this method for imaging biological specimens by imaging a Drosophila melanogaster sample.