The generator matrix 1 0 1 1 1 X^2+X 1 X^3+X^2 1 1 1 X^3+X 1 1 X^3 1 X^3+X^2+X 1 1 1 X^2 1 1 X 1 1 0 1 X^2+X 1 1 0 1 1 X^2+X 1 1 X 1 1 X^2 1 1 X^2 1 1 X X 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 X^3+X 1 1 X^2+X 1 X^3+X^2+X 0 1 1 1 1 0 1 1 0 1 X+1 X^2+X X^2+1 1 X^3+1 1 X^3+X^2 X+1 X^3+X 1 X^3+X^2+X+1 X^3 1 X^3+X^2+X 1 X^3+X^2+1 X^2+X+1 X^2 1 X 1 1 0 X+1 1 X^2+X 1 X^3+X^2+X+1 X^3+X^2+1 1 0 X 1 X^3+X+1 1 1 X^2 X^2+X 1 X^3+X^2+X+1 X^2 1 X^2+1 X 1 X X^3+1 X X^2+1 X^2+X+1 X^2+1 X^3+X^2+X+1 X^3+X^2+X+1 1 X^3+1 X^3+X+1 1 X^2+X+1 X^3+X^2+X+1 X^2+1 X+1 X^3+1 1 X^3+X^2+X+1 X^2+1 X+1 X^3+1 0 1 X 1 1 X^2+X+1 1 X^3 1 X^2 X^3+X^2 X^3+X X+1 X^2+1 1 X^3+X^2 X^3+X^2+X+1 0 0 X^2 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 0 0 0 X^3 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 0 0 X^3 0 0 X^3+X^2 X^3 X^3 X^3+X^2 X^3 0 0 X^2 X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^2 0 0 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 0 0 X^3 X^3+X^2 X^3+X^2 X^3 0 0 X^3+X^2 X^3 0 X^3 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 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 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 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 0 X^3 X^3 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 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 0 0 0 0 0 0 0 0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 generates a code of length 86 over Z2[X]/(X^4) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+126x^81+346x^82+462x^83+478x^84+522x^85+482x^86+428x^87+434x^88+318x^89+219x^90+128x^91+61x^92+50x^93+18x^94+4x^95+1x^96+8x^97+4x^98+2x^106+2x^107+1x^122+1x^124 The gray image is a linear code over GF(2) with n=688, k=12 and d=324. This code was found by Heurico 1.16 in 0.985 seconds.