  The boundary algebraic Bethe Ansatz for a supersymmetric nineteen
vertex-model constructed from a three-dimensional representation of the twisted
quantum affine Lie superalgebra $U_{q}[\mathrm{osp}(2|2)^{(2)}]$ is presented.
The eigenvalues and eigenvectors of Sklyanin's transfer matrix, with diagonal
reflection $K$-matrices, are calculated and the corresponding Bethe Ansatz
equations are obtained.
