In this Letter, we present an advanced optical configuration of coded aperture correlation holography (COACH) with a diffractive objective lens. Four-dimensional imaging of objects at the three spatial dimensions and with an additional spectral dimension is demonstrated. A hologram of three-dimensional objects illuminated by different wavelengths was recorded by the interference of light diffracted from the objects with the light diffracted from the same objects, but through a random-like coded phase mask (CPM). A library of holograms denoted point spread function (PSF) holograms were prerecorded with the same CPM, and under identical conditions, using point objects along different axial locations and for the different illuminating wavelengths. The correlation of the object hologram with the PSF hologram recorded using a particular wavelength, and at a particular axial location, reconstructs only the object corresponding to the particular axial plane and to the specific wavelength. The reconstruction results are compared with regular imaging and with another well-established holographic technique called Fresnel incoherent correlation holography.