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 X 1 1 1 1 1 X X 1 1 1 X^3+X^2 1 1 0 X 1 1 X X 1 1 X^3+X^2 1 0 X X 1 1 X X X 1 X 0 X 0 X 0 X^3 X^3+X X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X 0 X^3+X^2 X X^3+X^2+X X 0 X^3 X 0 X^2+X X^2+X X^3+X^2+X X^3+X^2 X^2 X^3+X^2 X^3+X^2+X 0 X^3+X X^3 X X^2 X^3+X X^3+X^2+X X^3+X^2+X X X^3+X^2 X^2 X^3+X X^3 X^2 X^3 X 0 X^2 X^3+X^2+X X X X^2 X^2 X^2+X X X^3+X^2 X^3+X^2 X^3+X^2+X X^2+X X 0 0 X^3 X^2 X X^3+X^2+X 0 X^3+X X^2+X X^3 0 X^2 X X^3+X^2 X^3+X^2+X X X^2+X X^3 X^3+X^2 X^3+X^2+X X^3 X 0 0 X X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2 X^3+X^2+X X 0 X^3 X^3+X^2+X X^3+X X^2 0 X^3+X X X^2 X^3+X^2+X X X^2 X^2 X^2+X X^3+X^2+X X^3 X^3+X X^3+X^2 X^2+X 0 X^3 X^3+X X^3 0 X^3+X X^3+X X^3+X^2 X^3+X^2+X X X^3 X^3 X X^3+X^2+X 0 X^2 X^2+X X^3 X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X X^3+X^2 X^2 X^3+X^2+X X^2+X X^2 X^3+X X^3 X^2 X^3+X^2 0 X^3+X X^2+X X X^3+X^2+X X^2+X 0 X^3 0 X X^3 X 0 X^3 X^2+X X^3+X^2 X^3+X^2+X 0 X^3+X^2+X X^2+X X^3+X^2+X X X^3+X^2 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 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 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 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+392x^79+113x^80+468x^81+426x^82+336x^83+737x^84+400x^85+396x^86+352x^87+98x^88+212x^89+10x^90+96x^91+7x^92+24x^93+8x^95+3x^96+16x^97+1x^136 The gray image is a linear code over GF(2) with n=672, k=12 and d=316. This code was found by Heurico 1.16 in 50.7 seconds.