The nearest-neighbour-interaction spin-1 Ising spin glass, in the presence of a random crystal field, is considered on diamond hierarchical lattices of fractal dimensions d = 2, 3 and 4. The coupling constants and crystal fields follow Gaussian probability distributions, which are taken as independent, at the beginning of the iteration process. By monitoring simultaneously the evolution of two probability distributions, associated respectively with the renormalized coupling constants and crystal fields, the phase diagrams of the model are obtained. A spin-glass phase, at finite temperatures, is found for hierarchical lattices with d = 3 and 4, but not for d = 2. Two distinct attractors characterized by zero effective coupling constants are detected. Following the usual procedure, i.e. associating an equilibrium phase with each basin of attraction, one obtains two phases with absence of magnetic order, namely, a zero-spin phase (where the spins prefer the 0 state) and a ±1-spin phase (where the spins prefer ±1 states at random).