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 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 X^3 1 1 X 1 1 1 1 1 1 X X 1 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^2 X^3 X^3+X^2 X^3+X^2 0 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 X^3+X^2 0 0 X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3 X^2 X^3 0 X^2 0 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 0 0 0 X^3 X^3+X^2 X^2 0 X^3 X^3 X^3+X^2 X^2 0 0 0 X^3 X^3 0 0 X^3+X^2 X^3+X^2 X^3+X^2 0 0 0 X^3 0 0 0 0 0 X^3 0 0 0 X^3 0 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 0 0 0 0 X^3 0 0 0 0 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 0 0 0 0 X^3 0 X^3 0 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 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 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+12x^70+22x^71+42x^72+50x^73+76x^74+92x^75+584x^76+398x^77+548x^78+92x^79+12x^80+30x^81+4x^82+28x^83+18x^85+22x^87+16x^89+1x^144 The gray image is a linear code over GF(2) with n=616, k=11 and d=280. This code was found by Heurico 1.16 in 0.609 seconds.