  We present ten metallicity measurements for quasar absorbers near $z=1.2$
that were selected for having unusually significant ZnII absorption in their
SDSS spectra. Follow-up UV space spectroscopy of the Ly$\alpha$ region shows
that all ten have damped Ly$\alpha$ (DLA) absorption, corresponding to neutral
hydrogen column densities in the range $2.4\times 10^{20}$ $\le$ N(HI) $\le$
$2.5\times 10^{21}$ atoms cm$^{-2}$, and indicating that the gas is very
optically thick and essentially neutral. The sample is a very small subset of
systems compiled by searching the University of Pittsburgh catalog of $\approx
30,000$ intervening MgII absorption line systems in SDSS quasar spectra up to
DR7. We started by isolating $\approx 3,000$ that had strong MgII absorption in
the redshift interval $1.0 < z < 1.5$ in brighter background quasars. Of these,
36 exhibited significant absorption near ZnII. Space UV spectroscopy was then
obtained for nine of these (25% of the total), and a tenth system in a fainter
quasar was found in the HST archives. The result is a representative sample of
the highest Zn$^+$ columns of gas within the DLA population. These
ZnII-selected systems define the upper envelope of DLA metallicities near
$z=1.2$. They show a tight anti-correlation between N(HI) and [Zn/H], with the
higher metallicity systems clearly exhibiting more depletion based on [Cr/Zn]
values. The various metal-line measurements (Zn, Cr, Si, Fe, Mn) indicate
evolved neutral gas with $-0.9 \le$ [Zn/H] $\le +0.4$.
