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 1 1 1 1 X^2 1 1 1 1 1 1 1 0 X 0 X^2+X X^2 X^3+X^2+X X^3+X^2 X X^2 X^2+X X^3 X^3+X 0 X^2+X X^2 X 0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X X^3 X^3+X^2+X X^2 X X^2 X X^3 X^3+X^2+X 0 X^2+X 0 X^2+X X^2 X X^3+X^2 X^3+X 0 X^2+X 0 X^2+X X^2 X X^2 X X^3+X^2 X^3+X X^3+X^2 X X^3+X X^3+X^2 X^2 X^3+X 0 X^3 X^2+X X^3+X^2+X X^3 X^3+X^2+X 0 X^2+X 0 X^3 X^3 0 X^2+X X^3+X^2+X X^3+X^2+X X^2+X X^3 X^3 X^2+X X^3+X^2+X X^2+X X^3 X^3 X^3+X^2 X^3+X X^3+X X^3+X X^3+X X^3+X^2 X^3+X^2+X X^3+X^2 0 0 X^3+X^2 0 X^2 X^2 0 X^2 X^3+X^2 0 X^2 0 0 X^3+X^2 0 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 X^3 X^3 X^3 X^2 X^2 X^3+X^2 X^3+X^2 0 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 0 0 0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 0 X^3+X^2 X^2 0 X^2 X^3+X^2 0 X^3 X^3 X^2 X^3 X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^2 X^2 0 X^3+X^2 X^3 X^3 X^2 0 X^3+X^2 0 X^3+X^2 X^2 0 0 0 0 X^3+X^2 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 0 0 0 0 X^3 0 0 0 0 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 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 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 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+47x^82+80x^83+100x^84+32x^85+498x^86+544x^87+497x^88+32x^89+83x^90+80x^91+41x^92+12x^94+1x^172 The gray image is a linear code over GF(2) with n=696, k=11 and d=328. This code was found by Heurico 1.16 in 1.13 seconds.