  The hot gas in galaxy halos may account for a significant fraction of missing
baryons in galaxies, and some of these gases can be traced by high ionization
absorption systems in QSO UV spectra. Using high S/N ratio $ HST$/COS spectra,
we discovered a high ionization state system at $z=1.1912$ in the sightline
toward \object{LBQS 1435-0134}, and two-components absorption lines are matched
for Mg X, Ne VIII, Ne VI, O VI, Ne V, O V, Ne IV, O IV, N IV, O III, and H I.
Mg X, detected for the first time ($5.8 \sigma$), is a particularly direct
tracer of hot galactic halos, as its peak ion fraction occurs near
$10^{6.1}\rm~ K$, about the temperature of a virialized hot galaxy halo of mass
$\sim 0.5 M^*$. With Mg X and NeVIII, a photoionization model cannot reproduce
the observed column densities with path lengths of galaxy halos. For
collisional ionization models, one or two temperature models do not produce
acceptable fits, but a three temperature model or a power law model can produce
the observed results. In the power law model, ${\rm d}N/{\rm d}T = 10^{4.4\pm
2.2-[Z/X]} T^{1.55\pm 0.41}$ with temperatures in the range $10^{4.39\pm0.13}
{\rm~K} < T < 10^{6.04\pm0.05}~ {\rm K}$, the total hydrogen column density is
$8.2 \times 10^{19} (0.3Z_{\odot}/Z) \rm~ cm^{-2}$ and the positive power law
index indicates most of the mass is at the high temperature end. We suggest
that this absorption system is a hot volume-filled galaxy halo rather than
interaction layers between the hot halo and cool clouds. The temperature
dependence of the column density is likely due to the local mixture of multiple
phase gases.
