  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
$(1.38\pm0.07)\cdot10^{-2}$ counts$/($keV$\cdot$kg$\cdot$yr$)$ in the
$0\nu\beta\beta$ decay region of interest and, with a total exposure of 372.5
kg$\cdot$yr, we attain a median exclusion sensitivity of $1.7\cdot10^{25}$ yr.
We find no evidence for $0\nu\beta\beta$ decay and set a $90\%$ CI Bayesian
lower limit of $3.2\cdot10^{25}$ yr on the $^{130}$Te half-life for this
process. In the hypothesis that $0\nu\beta\beta$ 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.
