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 22 GHz (wavelength λ = 1.3 cm). 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 70,833 km (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 μas, the highest for this source to date. This enabled us to estimate the size of the radio core to be 2.2 × 1013 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 δ ∼ 25 reported for 0716+714.