A single-screen model of the gravitational lens system 2016+112 is proposed, that explains recent Hubble Space Telescope} (HST) infrared (NICMOS-F160W) observations and new high-resolution European VLBI Network (EVN) 5-GHz radio observations, presented in this paper. In particular, we find that a massive `dark structure at the lens position, previously suggested by X-ray, optical and spectroscopic observations of the field around 2016+112, is not necessarily required to accommodate the strong lensing constraints. A massive structure to the north-west of the lens system, suggested from a weak-lensing analysis of the field, is included in the model. The lensed source is an X-ray bright active galaxy at z=3.273 with a central bright optical continuum core and strong narrow emission lines, suggestive of a type-II quasar. The EVN 5-GHz radio maps show a radio-jet structure with at least two compact subcomponents. We propose that the diamond caustic crosses the counter-jet of the radio source, so that part of the counter-jet, host galaxy and narrow-line emission regions are quadruply imaged. The remainder of the radio source, including the core, is doubly imaged. Our lens model predicts a very high magnification (mu~300) at the bightness peaks of the inner two radio components of complex C. If the jet exhibits relativistic velocities on micro-arsecond scales, it might result in apparent hyperluminal motion. However, the lack of strong radio variability and the peaked radio spectrum imply that these motions need not be present in the source. Our model furthermore implies that the optical spectrum of C can only show features of the AGN and its host galaxy.
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