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 ($xleq 7.5%$) 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.
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