  The parametric error on the QCD-coupling can be a dominant source of
uncertainty in several important observables. One way to extract the coupling
is to compare high order perturbative computations with lattice evaluated
moments of heavy quark two-point functions. The truncation of the perturbative
series is a sizable systematic uncertainty that needs to be under control. In
this contribution we give an update on our study arXiv:hep-lat/2203.07936v1 on
this issue. We measure pseudo-scalar two-point functions in volumes of $L=2$ fm
with twisted-mass Wilson fermions in the quenched approximation. We use full
twist, the non-perturbative clover term and lattice spacings down to $a=0.010$
fm to tame the large discretization effects. Our results show that both the
continuum extrapolations and the extrapolation of the $\Lambda$-parameter to
the asymptotic perturbative region are very challenging.
