A cadmium tungstate crystal boule enriched in $^{116}$Cd to 82% with mass of 1868 g was grown by the low-thermal-gradient Czochralski technique. The isotopic composition of cadmium and the trace contamination of the crystal were estimated by High Resolution Inductively Coupled Plasma Mass-Spectrometry. The crystal scintillators produced from the boule were subjected to characterization that included measurements of transmittance and energy resolution. A low background scintillation detector with two $^{116}$CdWO$_4$ crystal scintillators (586 g and 589 g) was developed. The detector was running over 1727 h deep underground at the Gran Sasso National Laboratories of the INFN (Italy), which allowed to estimate the radioactive contamination of the enriched crystal scintillators. The radiopurity of a third $^{116}$CdWO$_4$ sample (326 g) was tested with the help of ultra-low background high purity germanium $gamma$ detector. Monte Carlo simulations of double $beta$ processes in $^{116}$Cd were used to estimate the sensitivity of an experiment to search for double $beta$ decay of $^{116}$Cd.
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