  Minkowski proved that any $n$-dimensional lattice of unit determinant has a
nonzero vector of Euclidean norm at most $\sqrt{n}$; in fact, there are
$2^{\Omega(n)}$ such lattice vectors. Lattices whose minimum distances come
close to Minkowski's bound provide excellent sphere packings and
error-correcting codes in $\mathbb{R}^{n}$.
  The focus of this work is a certain family of efficiently constructible
$n$-dimensional lattices due to Barnes and Sloane, whose minimum distances are
within an $O(\sqrt{\log n})$ factor of Minkowski's bound. Our primary
contribution is a polynomial-time algorithm that list decodes this family to
distances approaching $1/\sqrt{2}$ of the minimum distance. The main technique
is to decode Reed-Solomon codes under error measured in the Euclidean norm,
using the Koetter-Vardy "soft decision" variant of the Guruswami-Sudan
list-decoding algorithm.
