The generator matrix 1 0 1 1 1 X^2+X 1 1 0 X^2+X 1 1 1 X^2 1 1 X 1 1 1 X^2 1 X 1 1 1 X 1 X X^2+X 1 1 X 0 0 1 1 1 1 X^2 1 1 1 1 X^2+X X 1 1 X 1 X^2+X 1 X^2+X 1 1 1 0 X^2 1 1 1 X 1 0 X^2 1 X^2+X 1 1 1 1 1 1 X^2+X X^2 1 0 1 1 0 1 1 X X^2+X+1 1 1 X^2+X+1 X^2+X 1 1 0 X 1 X^2+1 X^2 X+1 1 X 1 1 X^2+X+1 X^2+X 1 X^2 1 1 1 X 1 1 1 X^2+1 X^2 1 X^2+1 1 X^2+X X^2+X+1 X X^2 1 1 1 1 1 X^2+X+1 1 X^2+X 1 X^2 X^2+X+1 0 1 1 X^2 X^2+X+1 X 1 0 1 X 1 1 0 1 X^2+1 X^2+X X^2+X+1 0 1 1 X^2 0 0 X 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2+X X^2+X X X X X^2+X X X^2+X X X X X^2+X X^2 X^2+X X^2+X X X X^2 X X^2+X X^2+X X X X X X^2+X X X^2 X^2+X X^2 X^2+X X X X X^2+X X^2+X X^2 X^2 X^2 0 X X^2+X X^2+X X^2 X 0 X X^2 X 0 X^2+X X^2 X 0 0 0 X 0 0 X X^2 X X^2+X X X^2 X^2+X X X X^2 0 X 0 0 X^2 X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X 0 X X^2 X^2+X 0 0 X^2 X X^2 X^2 X X X^2+X X^2+X 0 X X^2 X 0 X X 0 0 X^2+X X 0 X X^2+X X^2+X X X^2+X X^2 X^2+X X^2 0 X^2+X X^2+X X 0 0 X X^2 X^2 X^2 0 X^2+X X 0 0 0 0 X 0 0 X X X^2+X X^2 X^2 X^2 X^2 X^2+X X^2+X X X^2+X X X^2 X X 0 X X^2+X 0 0 X^2 0 X X^2 0 X^2+X X 0 0 X X^2+X X^2 X^2 0 0 0 X^2+X X^2+X X X^2 X^2 0 X^2+X X X^2+X X X^2 X^2+X 0 0 X^2+X X^2+X 0 X^2 0 X^2 X^2+X X^2+X X X^2+X X X^2+X X^2+X X^2+X X 0 X^2 X^2 X 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 67. Homogenous weight enumerator: w(x)=1x^0+54x^67+148x^68+222x^69+367x^70+474x^71+560x^72+644x^73+661x^74+740x^75+725x^76+680x^77+635x^78+570x^79+527x^80+422x^81+251x^82+160x^83+122x^84+60x^85+58x^86+32x^87+18x^88+14x^89+12x^90+14x^91+8x^92+6x^93+4x^95+1x^96+1x^100+1x^104 The gray image is a linear code over GF(2) with n=304, k=13 and d=134. This code was found by Heurico 1.16 in 5.35 seconds.