  A generic heavy Higgs has both dim-4 and effective dim-6 interactions with
the Standard Model (SM) particles. The former has been the focus of LHC
searches in all major Higgs production channels, just as the SM one, but with
negative results so far. If the heavy Higgs is connected with Beyond Standard
Model (BSM) physics at a few TeV scale, its dim-6 operators will play a very
important role - they significantly enhance the Higgs momentum, and reduce the
SM background in a special phase space corner to a level such that a heavy
Higgs emerges, which is not possible with dim-4 operators only. We focus on the
associated VH production channel, where the effect of dim-6 operators is the
largest and the SM background is the lowest. Main search regions for this type
of signal are identified, and substructure variables of boosted jets are
employed to enhance the signal from backgrounds. The parameter space of these
operators are scanned over, and expected exclusion regions with 300 fb$^{-1}$
and 3 ab$^{-1}$ LHC data are shown, if no BSM is present. The strategy given in
this paper will shed light on a heavy Higgs which may be otherwise hiding in
the present and future LHC data.
