The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 0 X 0 X 0 0 X^2+X X^2+X 0 0 X X^2+X 0 0 X^2+X X^2+X X^2 X^2 X^2+X X 0 X^2 X X X^2 0 X^2+X X^2+X X^2 X^2+X 0 X X^2 X^2+X X^2 X^2 0 X^2 X^2+X X^2+X X X^2 X^2+X X^2+X X X 0 X^2 X^2 X X X X^2+X X^2 0 0 X X 0 X^2+X X^2+X 0 0 X^2+X X 0 0 X X 0 X^2 X X^2 X^2+X X^2 X 0 X X X^2 X^2 X^2+X X 0 X^2 X^2+X 0 X X^2 X^2+X X^2+X X^2 X X^2 X^2 X^2+X X X^2 X^2 X^2 X^2 X^2 0 X X X^2+X X^2+X X 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 50. Homogenous weight enumerator: w(x)=1x^0+23x^50+22x^51+26x^52+108x^53+158x^54+104x^55+29x^56+20x^57+10x^58+2x^59+8x^60+1x^106 The gray image is a linear code over GF(2) with n=216, k=9 and d=100. This code was found by Heurico 1.16 in 0.0918 seconds.