The generator matrix 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 1 X^2+X 1 0 1 1 1 X^3+X^2 1 X^3+X 1 1 1 0 1 X^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 1 1 1 1 1 1 0 1 X 1 1 X^2+X 1 X^3+X^2 1 1 1 1 1 1 X 1 X^3+X^2 1 0 X^3+X^2 1 1 X^3+X^2+X X X 1 0 1 X+1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X 1 X^3+1 X+1 X^2+1 0 1 X^2+X 1 X^3+X^2+X+1 X^3+1 X^3+X^2 1 X^3+X 1 X+1 X^2+1 0 1 X^2+X 1 X^3+1 X^3+X^2+X+1 1 X^3+X^2 1 X+1 X^2+1 X^3+X X^3+X^2+X+1 0 X^3+1 X^3+X^2+1 1 X+1 1 X^3+X+1 X^3+X X^2+1 X^2+X 1 X^3+X^2 1 X^3+X^2+X+1 X^2+X+1 X^3+X+1 X^3+X^2+1 X^2+1 X^3+1 X^2+X 0 1 X^3+X^2+1 X X X^3+X^2+1 X^2+X 1 X^2 X^3+X^2 0 0 0 X^3 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 X^3 0 0 0 0 0 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 generates a code of length 70 over Z2[X]/(X^4) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+18x^64+144x^65+352x^66+342x^67+442x^68+496x^69+586x^70+486x^71+447x^72+296x^73+260x^74+122x^75+49x^76+24x^77+16x^78+10x^79+1x^80+1x^92+2x^94+1x^104 The gray image is a linear code over GF(2) with n=560, k=12 and d=256. This code was found by Heurico 1.16 in 0.438 seconds.