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Computation of reduced Grobner basis

Currently I am reading one research paper http://www.ijpam.eu/contents/2010-62-4/11/11.pdf on page 486 equation 9 and 10 are describing an ideal, whereas on page 487 , Grobner basis has been calculated w.r.t ideal associated with ternary Goaly code.I understood the proof on page 486, but unable to compute the Grobner basis by using sage.