Before revision:  This is breaking thekissing number barrier of 3^n that is inherent in the previous best approaches tackling this problem . We obtain this improvement by incorporating a bound on the number of scaled hypercubes that are necessary to cover the \ell_2-ball of radius \sqrt{n \ell_2.
After revision:  This is breaking thekissing number barrier matches the currently fastest constant factor approximation algorithm for the shortest vector problem w.r.t. \ell_2.