  Pressure-induced ordering close to a $z=1$ quantum critical point is studied
in the presence of bond disorder in the quantum spin system
(C$_4$H$_{12}$N$_2$)Cu$_2$(Cl$_{1-x}$Br$_{x}$)$_6$ (PHCX) by means of muon-spin
rotation and relaxation. As for the pure system
(C$_4$H$_{12}$N$_2$)Cu$_2$Cl$_6$, pressure allows PHCX with small levels of
disorder ($x\leq 7.5\%$) to be driven through a quantum critical point
separating a low-pressure quantum paramagnetic phase from magnetic order at
high pressures. However, the pressure-induced ordered state is highly
inhomogeneous for disorder concentrations $x>1\%$. This behavior might be
related to the formation of a quantum Griffiths phase above a critical disorder
concentration $7.5\%<x_{\rm c}<15\%$. Br-substitution increases the critical
pressure and suppresses critical temperatures and ordered moment sizes.

Strongly Correlated Electrons