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 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X^3 0 0 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 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 0 X^3 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 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 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 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 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 0 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 0 0 0 0 0 X^3 X^3 0 X^3 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 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+10x^82+77x^84+384x^85+12x^86+15x^88+10x^90+1x^108+2x^116 The gray image is a linear code over GF(2) with n=680, k=9 and d=328. This code was found by Heurico 1.16 in 0.437 seconds.