The generator matrix 1 0 0 1 1 1 0 1 0 1 1 1 X^2 0 X X^2 1 1 X 1 1 X^2+X 1 1 1 X 0 1 X^2+X 1 1 X 1 X^2+X 1 X^2+X X^2+X 1 1 1 X^2 1 0 1 0 0 1 1 1 0 X^2 1 0 1 1 1 1 1 X X^2+1 X^2+X X^2+1 X+1 1 X^2+X+1 X+1 X 1 X X 1 X+1 X^2 X^2+X 0 X^2 X^2+1 1 1 X^2+X+1 X^2+X+1 X X^2 0 0 0 1 1 X^2 1 X^2+1 X^2+1 1 1 X^2 X^2 X 1 X^2 X+1 X^2+X X+1 1 X X 1 X^2+1 X^2 X^2+X X+1 1 X^2+1 1 X^2 X^2+X+1 1 X 1 X^2+X+1 X 0 0 X^2+1 X^2+X+1 1 0 0 0 0 X 0 X^2 X^2 X^2 X^2+X X^2+X X^2+X X X X X^2 0 X^2 X^2 0 0 X X X 0 X^2+X X 0 X^2 0 X 0 X^2+X X^2+X X^2 X^2+X X^2 X X^2 0 X X 0 generates a code of length 42 over Z2[X]/(X^3) who´s minimum homogenous weight is 37. Homogenous weight enumerator: w(x)=1x^0+56x^37+165x^38+296x^39+258x^40+232x^41+274x^42+178x^43+137x^44+128x^45+121x^46+76x^47+47x^48+44x^49+16x^50+10x^51+5x^52+4x^57 The gray image is a linear code over GF(2) with n=168, k=11 and d=74. This code was found by Heurico 1.11 in 0.062 seconds.