In the view of exploring the inverted hierarchy region future experiments investigating the neutrinoless double beta decay have to demand for detectors with excellent energy resolution and zero background in the energy region of interest. Cryogenic scintillating bolometers are very suitable detectors for this task since they provide particle discrimination: the simultaneous detection of the phonon and light signal allows us to identify the interacting type of particle and thus guarantees a suppression of (Formula presented.)-induced backgrounds, the key-issue for next-generation tonne-scale bolometric experiments. The LUCIFER project aims at running the first array of enriched scintillating Zn(Formula presented.)Se bolometers (total mass of about 8kg of (Formula presented.)Se) with a background level as low as 10(Formula presented.) counts/(keV kg y) in the energy region of interest. The main effort is currently focused on the finalization of the crystal growth procedure in order to achieve high quality Zn(Formula presented.)Se crystals both in terms of radiopurity and bolometric properties. We present results from tests of such crystals operated at mK temperatures which demonstrate the excellent background rejection capabilities of this detection approach towards a background-free demonstrator experiment. Besides, the high purity of the enriched (Formula presented.)Se material allows us to establish the most stringent limits on the half-life of the double beta decay of (Formula presented.)Se on excited levels.