The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 1 1 1 X X^2 1 0 0 X^2+X X^2+X 1 1 0 X 1 1 1 1 X^2 1 1 0 X^2+X 1 1 X^2 1 X 1 1 0 1 0 0 0 0 X+1 X X^2 X+1 1 X^2 X^2+1 X+1 X^2+X+1 1 X 0 1 1 1 X 1 X+1 1 0 0 X^2 X^2+X+1 X X^2+X X X^2+X+1 1 1 0 X^2+X+1 X^2 1 0 X^2+X 0 0 0 1 0 0 0 1 X+1 1 X^2+1 X^2 X^2+1 X^2+X X^2+X+1 X^2+X X^2+1 X X^2 0 X^2+X+1 X 1 X^2+X+1 X^2+X X^2+X+1 1 X^2+X+1 X^2+X X X^2+1 0 0 X^2 X^2+X+1 X^2 1 X^2+X 1 X^2+1 1 X 0 0 0 0 1 0 1 X^2 X^2+1 1 X+1 X^2+1 X^2+X X^2 X^2+1 X+1 X 1 X+1 X^2+X+1 X X X^2 X^2+X X 1 1 X^2+X+1 X^2+X X^2+1 X^2 1 X^2+1 X^2+X X^2+1 1 X^2 1 X^2+X+1 X^2+X+1 X^2 X^2+X 0 0 0 0 0 1 1 X^2+1 X X+1 X^2+1 X^2+X X^2+1 0 X^2 X^2+X+1 X X^2+X+1 X 1 X^2+X+1 X+1 X+1 X^2 X^2+X+1 X+1 0 X^2 X+1 X+1 X X^2+1 X+1 X^2+1 X X^2+X X+1 X^2+X X^2+X X^2+X+1 X 1 0 0 0 0 0 0 X 0 X X X^2+X X X^2 0 X X 0 X^2+X X X^2 X^2+X X X^2+X X X^2+X X^2 X^2 0 0 X^2 X^2 X^2 0 0 X 0 X X^2+X X^2 X X^2+X X 0 generates a code of length 42 over Z2[X]/(X^3) who´s minimum homogenous weight is 32. Homogenous weight enumerator: w(x)=1x^0+96x^32+416x^33+970x^34+1894x^35+3161x^36+5090x^37+7624x^38+10124x^39+13155x^40+15060x^41+15496x^42+15236x^43+13141x^44+10596x^45+7863x^46+5044x^47+3014x^48+1604x^49+777x^50+398x^51+190x^52+66x^53+37x^54+8x^55+10x^56+1x^58 The gray image is a linear code over GF(2) with n=168, k=17 and d=64. This code was found by Heurico 1.13 in 111 seconds.