Matrices whose submatrices have determinant of at must 2

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Totally Unimodular matrices, for which every square submatrix has a determinant in $\{0,\pm 1\}$, are well-studied due to their usefulness in integer programming. Has there been any study of matrices whose submatrices have determinants in $\{0, \pm 1, \pm 2\}$? Are there any known useful classes of matrices with this property?