  We use a modified perturbative renormalization group approach to study the
random quantum antiferromagnetic spin-3/2 chain. We find that in the case of
rectangular distributions there is a quantum Griffiths phase and we obtain the
dynamical critical exponent $Z$ as a function of disorder. Only in the case of
extreme disorder, characterized by a power law distribution of exchange
couplings, we find evidence that a random singlet phase could be reached. We
discuss the differences between our results and those obtained by other
approaches.
