  A search is presented for a high-mass Higgs boson in the
$H\rightarrow\ell\ell\ell\ell$, $H\rightarrow\ell\ell\nu\nu$,
$H\rightarrow\ell\ell qq$, and $H\rightarrow\nu\nu qq$ decay modes using the
ATLAS detector at the CERN Large Hadron Collider. The search uses proton-proton
collision data at a centre-of-mass energy of 8 TeV corresponding to an
integrated luminosity of 20.3 fb$^{-1}$. The results of the search are
interpreted in the scenario of a heavy Higgs boson with a width that is small
compared with the experimental mass resolution. The Higgs boson mass range
considered extends up to 1 TeV for all four decay modes and down to as low as
140 GeV, depending on the decay mode. No significant excess of events over the
Standard Model prediction is found. A simultaneous fit to the four decay modes
yields upper limits on the production cross-section of a heavy Higgs boson
times the branching ratio to Z boson pairs. 95% confidence level upper limits
range from 0.53 pb at $m_H=195$ GeV to 0.008 pb at $m_H=950$ GeV for the
gluon-fusion production mode and from 0.31 pb at $m_H=195$ GeV to 0.009 pb at
$m_H=950$ GeV for the vector-boson-fusion production mode. The results are also
interpreted in the context of Type-I and Type-II two-Higgs-doublet models.
