  We present results on 4-lepton + 2-jet production, the partonic processes
most commonly described as vector boson pair production in the Vector Boson
Fusion (VBF) mode. This final state contains diagrams that are mediated by
Higgs boson exchange. We focus particularly on the high-mass behaviour of the
Higgs boson mediated diagrams, which unlike on-shell production, gives
information about the Higgs couplings without assumptions on the Higgs boson
total width. We assess the sensitivity of the high-mass region to Higgs
coupling strengths, considering all vector boson pair channels, $W^-W^+$,
$W^\pm W^\pm$, $W^\pm Z$ and $ZZ$. Because of the small background, the most
promising mode is $W^+ W^+$ which has sensitivity to Higgs couplings because of
Higgs boson exchange in the $t$-channel. Using the Caola-Melnikov (CM) method,
the off-shell couplings can be interpreted as bounds on the Higgs boson total
width. We estimate the bound that can be obtained with current data, as well as
the bounds that could be obtained at $\sqrt{s}=13$~TeV in the VBF channel for
data samples of 100 and 300 fb$^{-1}$. The CM method has already been
successfully applied in the gluon fusion (GGF) production channel. The VBF
production channel gives important complementary information, because both
production and decay of the Higgs boson occur already at tree graph level.
