We report new results from the search for neutrinoless double-beta decay in $^{130}$Te with the CUORE detector. This search benefits from a four-fold increase in exposure, lower trigger thresholds and analysis improvements relative to our previous results. We observe a background of $(1.38pm0.07)cdot10^{-2}$ counts$/($keV$cdot$kg$cdot$yr$)$ in the $0 ubetabeta$ decay region of interest and, with a total exposure of 372.5 kg$cdot$yr, we attain a median exclusion sensitivity of $1.7cdot10^{25}$ yr. We find no evidence for $0 ubetabeta$ decay and set a $90%$ CI Bayesian lower limit of $3.2cdot10^{25}$ yr on the $^{130}$Te half-life for this process. In the hypothesis that $0 ubetabeta$ decay is mediated by light Majorana neutrinos, this results in an upper limit on the effective Majorana mass of 75-350 meV, depending on the nuclear matrix elements used.
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