The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 X 0 2X 1 1 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 0 2 1 X 2X+1 2 1 2X+1 1 1 1 0 0 0 0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X X X X 2X 2X 2X 2X X 0 0 0 0 0 X 0 0 0 0 X 2X X 2X X 2X 2X 0 0 X 2X 0 X 2X 0 0 X 0 0 0 0 0 0 X 0 0 X 2X 2X X X 0 2X 2X 2X 2X 2X 2X X 0 0 0 0 X X 0 0 0 0 0 0 2X 0 2X X 0 X X 2X 2X X 2X 0 0 0 X 2X 0 0 2X 0 2X 0 0 0 0 0 0 0 X 2X 0 2X 2X X X 2X 2X X 2X X X X 2X 2X 2X 0 2X 2X 0 generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 39. Homogenous weight enumerator: w(x)=1x^0+54x^39+24x^41+144x^42+270x^44+296x^45+774x^47+616x^48+2256x^50+1238x^51+3564x^53+1706x^54+3816x^56+1426x^57+1986x^59+686x^60+432x^62+222x^63+118x^66+38x^69+16x^72 The gray image is a linear code over GF(3) with n=81, k=9 and d=39. This code was found by Heurico 1.16 in 1.78 seconds.