  The cross section of the process $e^+e^-\to \pi^+D^0D^{*-}$ for
center-of-mass energies from 4.05 to 4.60~GeV is measured precisely using data
samples collected with the BESIII detector operating at the BEPCII storage
ring.
  Two enhancements are clearly visible in the cross section around 4.23 and
4.40~GeV.
  Using several models to describe the dressed cross section yields stable
parameters for the first enhancement, which has a mass of $4228.6 \pm 4.1 \pm
6.3 \un{MeV}/c^2$ and a width of $77.0 \pm 6.8 \pm 6.3 \un{MeV}$, where the
first uncertainties are statistical and the second ones are systematic.
  Our resonant mass is consistent with previous observations of the $Y(4220)$
state and the theoretical prediction of a $D\bar{D}_1(2420)$ molecule.
  This result is the first observation of $Y(4220)$ associated with an
open-charm final state.
  Fits with three resonance functions with additional $Y(4260)$, $Y(4320)$,
$Y(4360)$, $\psi(4415)$, or a new resonance, do not show significant
contributions from either of these resonances. The second enhancement is not
from a single known resonance. It could contain contributions from $\psi(4415)$
and other resonances, and a detailed amplitude analysis is required to better
understand this enhancement.
