The generator matrix 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 0 1 1 X^2+X X^3+X^2 1 1 1 1 X^3+X 1 1 0 1 1 X^2+X X^3+X 1 1 1 X^3+X^2 1 1 1 0 1 1 X^2+X 1 1 X^3+X^2 1 1 X^3+X 1 1 X X X 0 X 1 X 1 1 X^3+X^2 1 X^3+X^2+X X^3+X^2 X^3 X^2+X 1 1 1 1 1 1 1 X 1 0 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 0 X+1 1 X^2+X X^2+1 1 1 X^3+X^2 X^3+X^2+X+1 X^3+X X^3+1 1 X^2+X X+1 1 X^3+X^2 X^3+1 1 1 0 X^2+1 X^3+X 1 X^3+X^2+X+1 X^2+1 0 1 X^2+X X+1 1 X^3+X X^3+X^2+X+1 1 X^3+1 X^3+X^2 1 X^2 1 1 X^3 X X X^3+X^2 X^3+X^2+X X^2+X X^3+X+1 X+1 1 X^2+X 1 X 1 1 X^2+1 X^3+1 X^3+X 1 1 X^3+X^2+1 0 0 X^3+X 1 0 0 0 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 0 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+31x^70+212x^71+211x^72+534x^73+283x^74+680x^75+277x^76+686x^77+269x^78+484x^79+123x^80+178x^81+52x^82+32x^83+26x^84+10x^85+2x^86+1x^88+1x^90+1x^92+1x^94+1x^118 The gray image is a linear code over GF(2) with n=608, k=12 and d=280. This code was found by Heurico 1.16 in 0.516 seconds.