The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 2X 1 1 1 1 X 0 0 1 X 1 2X 1 1 1 2X 1 1 0 1 0 0 X 2X+1 2X+1 2X+2 2 1 2 2X 1 1 2X+2 2 2X 1 1 2X 1 1 0 0 X 2X+2 1 1 X 2X 0 0 1 1 2X+2 2X X+2 2X+1 2 X+1 0 2X+1 X 1 X+1 2 0 2X+1 2X+2 1 2X 2X+2 X+2 1 0 2X X+2 X+1 2 1 0 0 0 2X 2X 0 2X X X 2X 2X 0 X X 0 0 X 2X 2X 2X 2X 0 X X X X 0 0 0 X generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+360x^54+560x^57+464x^60+384x^63+340x^66+76x^69+2x^72 The gray image is a linear code over GF(3) with n=90, k=7 and d=54. This code was found by Heurico 1.13 in 0.0163 seconds.