We present new imaging observations of the remnant of Supernova ( SN ) 1987A at 44 GHz , performed in 2011 with the Australia Telescope Compact Array ( ATCA ) . The 0 \hbox { $ . ^ { \prime \prime } $ } 35 \times 0 \hbox { $ . ^ { \prime \prime } $ } 23 resolution of the diffraction-limited image is the highest achieved to date in high-dynamic range . We also present a new ATCA image at 18 GHz derived from 2011 observations , which is super-resolved to 0 \hbox { $ . ^ { \prime \prime } $ } 25 . The flux density is 40 \pm 2 mJy at 44 GHz and 81 \pm 6 mJy at 18 GHz . At both frequencies , the remnant exhibits a ring-like emission with two prominent lobes , and an east-west brightness asymmetry that peaks on the eastern lobe . A central feature of fainter emission appears at 44 GHz . A comparison with previous ATCA observations at 18 and 36 GHz highlights higher expansion velocities of the remnant eastern side . The 18–44 GHz spectral index is \alpha = -0.80 ( S _ { \nu } \propto \nu ^ { \alpha } ) . The spectral index map suggests slightly steeper values at the brightest sites on the eastern lobe , whereas flatter values are associated with the inner regions . The remnant morphology at 44 GHz generally matches the structure seen with contemporaneous X-ray and H \alpha observations . Unlike the H \alpha emission , both the radio and X-ray emission peaks on the eastern lobe . The regions of flatter spectral index align and partially overlap with the optically-visible ejecta . Simple free-free absorption models suggest that emission from a pulsar wind nebula or a compact source inside the remnant may now be detectable at high frequencies , or at low frequencies if there are holes in the ionised component of the ejecta .