Neutrinoless double-$beta$ decay ($0 ubetabeta$ decay) is a hypothetical process that can occur if the neutrino is its own antiparticle. The COBRA collaboration operates a demonstrator to search for these decays at the Laboratori Nazionali del Gran Sasso in Italy using CdZnTe semiconductor detectors. The exposure of $234.7,$kg,d considered in this analysis was collected between September 2011 and February 2015. The analysis focuses on the decay of the nuclides $^{114}$Cd, $^{128}$Te, $^{70}$Zn, $^{130}$Te and $^{116}$Cd. A Bayesian analysis is performed to estimate the signal strength of $0 ubetabeta$ decay. No signal is observed for any of these nuclides. Therefore, the following half-life limits at 90% credibility are set: $T_{1/2}^{0 u}>1.6cdot10^{21},$yr ($^{114}$Cd), $T_{1/2}^{0 u}>1.9cdot10^{21},$yr ($^{128}Te$), $T_{1/2}^{0 u}>6.8cdot10^{18},$yr ($^{70}$Zn), $T_{1/2}^{0 u}>6.1cdot10^{21},$yr ($^{130}$Te), and $T_{1/2}^{0 u}>1.1cdot10^{21},$yr ($^{116}$Cd).
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