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 X X^2 X^2 X X 0 0 0 X^2 X 1 X 0 1 1 X^2 X 1 X 1 0 X 0 X 0 0 0 0 0 0 0 0 X^2 X X X^2+X 0 X^2+X X^2+X 0 X X^2 X^2+X X^2 X X X X^2 X 0 X X^2 X^2+X X X^2+X X^2+X X^2+X X^2+X X X^2 0 X^2+X X^2+X X^2 X X^2+X X X 0 X 0 X^2+X X^2 0 X^2 X 0 X^2 X^2 X X^2 X^2+X X^2 0 X^2 X^2+X X^2 X^2 X^2 0 0 X 0 0 0 0 0 0 0 X^2+X X^2 X X X X 0 X 0 X X^2+X X^2 0 X^2+X X X X^2+X X^2+X X^2 0 X^2+X 0 X^2 X^2+X X 0 X^2 X^2 X 0 X^2 X X^2+X X^2+X X X^2 X^2 X X X X X^2 X X X X X^2 X^2 X^2 0 X X^2 X^2+X X X^2 X X^2 0 0 0 X 0 0 0 X X^2+X X X X^2+X 0 X X^2 0 X^2+X X^2+X X^2+X X^2 X^2+X X 0 X^2 0 X^2 X X X X^2 X 0 X^2+X 0 X X^2+X 0 X^2 X X X^2 X^2+X 0 X^2 X X X 0 0 0 0 X 0 X X^2 X^2 X^2 X^2+X X 0 0 0 X X^2 X X^2+X 0 0 0 0 0 X 0 X X X X^2 X X X X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X X^2+X X^2 X^2 X 0 X^2+X X^2 X^2+X X^2+X X X^2+X X 0 X^2+X X^2+X 0 0 X^2 X X^2 0 X^2+X X^2 X^2 0 X^2 X^2 X^2 X^2+X X^2 0 X X^2+X X^2+X X X^2+X X^2 X^2+X 0 X X^2+X 0 X X X^2+X 0 0 0 0 0 X X X^2 X^2+X X^2+X X X X^2+X 0 X X^2 X^2 X^2 X^2+X X 0 X^2 X^2 0 X 0 X X^2 X^2 X^2+X X^2+X X^2+X X^2+X 0 X^2 X^2 X^2 X^2 0 0 X^2+X X^2+X X^2+X X^2+X X 0 X 0 X X^2+X X X^2 X^2 X 0 0 X X X^2 X X^2+X X^2 X X 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+178x^56+530x^58+28x^59+799x^60+112x^61+1096x^62+472x^63+1549x^64+892x^65+1942x^66+1116x^67+2173x^68+892x^69+1558x^70+404x^71+1068x^72+148x^73+660x^74+24x^75+397x^76+4x^77+202x^78+4x^79+100x^80+28x^82+6x^84+1x^100 The gray image is a linear code over GF(2) with n=268, k=14 and d=112. This code was found by Heurico 1.16 in 22.2 seconds.