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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 X^2 0 X X^2 X 1 0 X X^3+X^2 X^2+X 0 X^2+X X^3+X^2 X^3+X X^2+X 0 X^3+X X^3+X^2 X^3 X^3+X X^2 X^2+X X^3+X^2+X 0 X^3+X^2 X^3+X 0 X^2+X X^3+X^2 X^3+X 0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X 0 X^2+X X^3+X^2 X^3+X X^2 X^3+X^2+X 0 X X^3 X^2+X X^2 X^3+X X^3 X^3+X^2+X X^3+X^2 X 0 X^3 X^2+X X^3+X^2+X X^3 X^2+X 0 X^3+X^2+X X^3+X^2 X^3+X^2 X^2 X^2 X^3+X X^3+X X X 0 0 X^3 X^3 X^2+X X^2+X X^3+X^2+X X^3+X^2+X 0 X^3 X^3 X^2+X X 0 X^3+X^2 X^2 X^3+X X^3+X^2 X^2+X X^3+X^2 0 0 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 0 0 X^3 generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 79. Homogenous weight enumerator: w(x)=1x^0+38x^79+213x^80+76x^81+236x^82+278x^83+378x^84+248x^85+258x^86+98x^87+174x^88+28x^89+15x^90+2x^91+2x^92+2x^94+1x^154 The gray image is a linear code over GF(2) with n=672, k=11 and d=316. This code was found by Heurico 1.16 in 0.75 seconds.