The generator matrix 1 0 0 1 1 1 0 1 X X^2 1 1 X 1 X^2+X X^2 X^2+X 1 1 1 1 X 1 1 X^2+X 1 1 X 0 1 1 X^2 X 1 1 1 1 X^2+X 1 1 1 X^2+X X 1 1 X X^2+X 0 1 0 X^2+X 1 X^2+X 0 X^2+X 1 1 X^2+X X^2 1 1 1 1 1 X^2 0 0 1 1 1 1 X 0 X^2+X X^2 X 0 1 0 0 1 1 1 X 1 X^2+X 1 X^2+X 1 X+1 X^2 1 1 X^2+1 X^2 X^2+X+1 X 1 0 X^2+X+1 1 X^2+X X+1 X^2+X 1 X+1 X^2 X^2+X 1 0 X+1 X^2+X+1 X^2+X 1 0 X^2+1 X^2+X X^2 1 1 0 1 1 1 X^2+1 1 X 0 1 1 1 X+1 X 1 1 X^2+X+1 X+1 X^2+X+1 X^2+X+1 X^2 X^2+X 1 1 X^2+X+1 X^2 X^2+1 X+1 1 X^2 1 1 X^2 0 0 1 X+1 X^2+X+1 0 X+1 1 X^2 1 X^2+1 0 1 X 1 X X+1 X X^2+1 X^2+1 X^2+X X X X^2+1 X^2+1 X^2+X+1 X^2 1 X^2+1 X^2+X+1 X^2+X 1 0 X+1 X X^2 0 X+1 X^2 X X 1 X X+1 1 X^2+X+1 X^2+X+1 X^2 1 X+1 1 X^2 X+1 X+1 X^2+1 X^2 X^2+1 X+1 X^2+1 X^2+X+1 X^2+X X^2+X 1 X^2+X+1 1 X^2 1 X X^2+X+1 X^2+1 X^2+X+1 X^2+X 1 X^2+X X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 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 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+390x^70+696x^72+862x^74+660x^76+554x^78+378x^80+282x^82+140x^84+72x^86+44x^88+16x^90+1x^96 The gray image is a linear code over GF(2) with n=304, k=12 and d=140. This code was found by Heurico 1.16 in 4.32 seconds.