  While it has recently been demonstrated how to certify the maximal amount of
randomness from any pure two-qubit entangled state in a device-independent way
[E. Woodhead et al., Phys. Rev. Research 2, 042028(R)(2020)], the problem of
optimal randomness certification from entangled states of higher local
dimension remains open. Here we introduce a method for device-independent
certification of the maximal possible amount of $2\log_23$ random bits using
pure bipartite entangled two-qutrit states and extremal nine-outcome general
non-projective measurements. To this aim, we exploit the extended Bell scenario
introduced recently in [S. Sarkar et al., arXiv:2110.15176], which combines a
device-independent method for certification of the full Weyl-Heisenberg basis
in three-dimensional Hilbert spaces together with a one-sided
device-independent method for certification of two-qutrit partially entangled
states.
