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In this paper we present an ideal for lattices in general form, including integer and non-integer lattices. Considering Gröbner bases of this ideal which is a toric ideal and using its characteristic. Gröbner bases for binary linear codes were introduced by Borges et al. We extend their work to non-binary group block codes. Using this Gröbner bases an algebraic method for finding the closest vector in lattices is presented.