We present RadioAstron Space VLBI imaging observations of the BL Lac object S5 0716+71 made on 2015 January 3-4 at a frequency of 22GHz (wavelength {lambda}=1.3cm). The observations were made in the framework of the AGN Polarization Key Science Program. The source was detected on projected space-ground baselines up to 70833km (5.6 Earth diameters) for both parallel-hand and cross-hand interferometric visibilities. We have used these detections to obtain a full-polarimetric image of the blazar at an unprecedented angular resolution of 24{mu}as, the highest for this source to date. This enabled us to estimate the size of the radio core to be 2.2x10^13^K for the blazar core. This implies that the inverse-Compton limit must be violated in the rest frame of the source, even for the largest Doppler factor {delta}~25 reported for 0716+714.