X-ray phase contrast imaging (XPCI) is a newborn imaging technique providing high sensitivity for weakly absorbing objects. Measurement of the phase shifts of the X-rays waveform traveling through the inspected object enables to reach with lower dose substantially higher contrast than conventional absorption radiography. We propose and experimentally demonstrate a novel XPCI method using a coded aperture and a table-top nano-focus X-ray source. The method is based on the very precise determination of the position of the projected pattern downstreaming from the aperture directly from the image of the pattern. First experimental tests with multiple edge object (grating) used as coded aperture are presented.