  We investigate the current noise in HgTe-based quantum wells with an inverted
band structure in the regime of disordered edge transport. Consistent with
previous experiments, the edge resistance strongly exceeds $h/e^2$ and weakly
depends on the temperature. The shot noise is well below the Poissonian value
and characterized by the Fano factor with gate voltage and sample to sample
variations in the range $0.1<F<0.3$. Given the fact that our devices are
shorter than the most pessimistic estimate of the ballistic dephasing length,
these observations exclude the possibility of one-dimensional helical edge
transport. Instead, we suggest that a disordered multi-mode conduction is
responsible for the edge transport in our experiment.
