The generator matrix 1 0 0 1 1 1 0 X^3 1 1 X^3 X^2 1 1 1 1 X^3+X X^3+X 1 X^3+X^2+X 1 X^3+X X 1 X^3+X 1 1 1 X^3+X 1 1 1 X^2+X 1 1 X^3+X X 1 X^3+X^2 1 X^2 1 1 0 1 1 1 1 0 X^3+X^2 1 X^2 1 X^2 X^2+X 1 0 1 1 1 1 1 1 1 X^3+X^2 X 1 1 1 1 1 1 1 1 X^3 X^3+X 1 0 1 1 1 1 X^3+X^2 1 X^3+X X^3+X^2+X 1 0 1 0 0 X^2+1 X^2+1 1 X^3+X^2+X X^3 X^3+X^2+1 1 1 X^3+X^2 1 X^2+X X+1 1 X^2+X X 1 X^3+X^2+X+1 1 1 X^3+X^2+X+1 X^2 X+1 X X+1 1 X^2 X^3+X^2+X X^3+X^2 1 X^3+1 X^2+1 X^3+X 1 X^2+X+1 0 X 1 X^3+X+1 X^2 1 X^3+X^2+X X^3 X^3+X X^3+X^2+1 1 1 X^2+X+1 1 1 X^3+X 1 X^3+X^2+X+1 X^3+X X^3+1 X^3+X^2 X^3+X^2+X X^3+X X^3+X^2+X+1 X^3+X^2 X^2+X 1 0 X^3+X 0 X^2 1 1 X^2+X+1 X^3+X^2+X+1 X^3 X^3+X^2+X 1 X^3 X^2 X^2+1 X+1 X^2+1 X^3+X^2+X 1 0 1 1 X^3 0 0 1 X+1 X^3+X+1 X^3 X^3+X^2+X+1 1 X^3+X^2+X X^2+1 1 X^3+X X^3+X^2+1 X X^3+X+1 X^2 X^3+X^2+1 1 X X^2 X^2+X+1 X^3+X^2+X X+1 X^2+1 1 X^2+X X^2 X^3+X^2+X+1 X^3+X^2+X+1 X+1 X^2+1 X^3 1 X^3+1 X^3+X 1 X^2+X 0 1 X^3 X^2+1 X^2+1 X^3+X^2+1 X^3+X^2+X X^3+X^2+X+1 X^2 X^3+X^2+X X^3+X^2+X+1 X^2 X+1 X X^3+X X^3 1 X^3+X^2+1 X^3+X^2+1 1 X^2+1 X^2+X 1 X^3+X^2+X+1 X+1 X^3+X^2+X+1 X^3+X X^2+X+1 1 X+1 X^3+X+1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+X+1 1 X^2+X X^3+1 1 X^2 X 1 0 X^2+X 1 X^3+X^2+X X^3+X^2+1 X^2+X+1 X^3+X X^3+X^2+X X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 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+138x^82+726x^83+1112x^84+1160x^85+1019x^86+952x^87+752x^88+676x^89+468x^90+338x^91+276x^92+252x^93+137x^94+96x^95+49x^96+24x^97+12x^98+1x^100+2x^102+1x^108 The gray image is a linear code over GF(2) with n=696, k=13 and d=328. This code was found by Heurico 1.16 in 16.5 seconds.