The generator matrix 1 0 0 1 1 1 X 1 X^2+X 1 1 X^2 1 X^2+X X^2+X X^2 X^2 X 1 1 1 1 X X^2+X X^2+X 1 1 1 0 1 X 1 1 1 1 1 1 X^2 X^2 X 1 1 0 1 0 X^2 X^2+1 1 1 0 0 X^2 X^2+1 1 1 1 X^2+X X X^2+X 1 X X^2+X+1 X^2+X X+1 1 1 1 0 X^2+1 X^2 X 1 X^2 X+1 X+1 X^2+X+1 X 1 0 1 1 X^2+X X^2+X+1 X^2+X+1 0 0 1 X^2+X+1 X+1 X^2 X^2+1 X 1 1 X^2+1 X X^2+X X+1 1 1 1 X X X^2+X+1 X^2 X^2+1 X^2 X^2+1 X^2+X+1 1 X^2+X X+1 X^2+X 0 X^2+X 0 X^2+X X 1 X X^2 1 X^2+X X^2+X X^2+X 1 generates a code of length 42 over Z2[X]/(X^3) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+245x^40+136x^42+70x^44+12x^46+24x^48+20x^50+4x^52 The gray image is a linear code over GF(2) with n=168, k=9 and d=80. As d=80 is an upper bound for linear (168,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9. This code was found by Heurico 1.16 in 0.523 seconds.