The critical brain hypothesis states that the cortex operates near a continuous phase transition between absorbing and active states. At the critical point, the network spiking activity would be characterized by neuronal avalanches with size and duration probability distributions given by power laws with well-defined critical exponents. However, experimental measurements show multiple pairs of exponents for the size and duration avalanche distributions. A hypothesis to account for this phenomenon is that the brain dynamics is not critical but quasicritical, and a prediction of the theory is that the exponent pairs adhere to a dynamical scaling relation. On the other hand, experimental evidence suggests that cortical networks are organized according to a modular hierarchical architecture (HM). Here we study avalanches and critical behavior in a HM network model with fully connected intramodular topology and stochastic neurons of the Galves-Löcherbach type. The system has two mechanisms that make the critical region an attractor of its self-organized quasicritical (SOqC) dynamics: (i) dynamical gains, which adapt the neuronal firing rates, and (ii) dynamical synapses, which represent homeostatic mechanisms. We characterize the size and duration distributions of the avalanches displayed by the model and calculate the scaling relation. The model seemingly exhibits quasicritical behavior.