We present updated results for the light-quark
connected part of the leading hadronic contribution to the
muon $g-2$ from configurations with 2+1+1 flavors of HISQ
quarks using the time-momentum representation of the
electromagnetic current correlator. We have added statistics
on two ensembles as well as a fourth lattice spacing
using configurations that have been generated by the MILC
collaboration at the physical pion mass. Additionally we account
for the leading finite-volume and taste-breaking effects
using Staggered Chiral Perturbation Theory at NNLO.
