Expanding the library of self-assembled superstructures provides insight into the behaviour of atomic crystals and supports the development of materials with mesoscale order(1,2). Here we build on recent findings of soft matter quasicrystals(3-6) and report a quasicrystalline binary nanocrystal superlattice that exhibits correlations in the form of partial matching rules reducing tiling disorder. We determine a three-dimensional structure model through electron tomography(7,8) and direct imaging of surface topography. The 12-fold rotational symmetry of the quasicrystal is broken in sublayers, forming a random tiling of rectangles, large triangles and small triangles with 6-fold symmetry. We analyse the geometry of the experimental tiling and discuss factors relevant for the stabilization of the quasicrystal. Our joint experimental-computational study demonstrates the power of nanocrystal superlattice engineering and further narrows the gap between the richness of crystal structures found with atoms and in soft matter assemblies.