Building on the works of Berthé-Steiner-Thuswaldner and Fogg-Nous we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the associated subshift satisfies the Boshernitzan criterion. As a consequence, we show that for these torus translations, every quasi-periodic potential can be approximated uniformly by one for which the associated Schrödinger operator has Cantor spectrum of zero Lebesgue measure. (Joint work with Jon Chaika, Jake Fillman, Philipp Gohlke)