The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X^2 X^2+X X X 1 X 1 0 1 X^2 1 X X^2 1 1 1 1 X^2+X X 1 X^2 X^2 1 X^2 1 X 1 1 1 X 1 1 1 X^2 1 X^2+X 1 1 1 1 0 1 X^2+X 0 0 0 1 X^2 X^2+X X^2+X 1 X^2+X 1 X 1 X X^2+X 1 1 X^2+X 0 X 1 X^2+X X X X^2+X 1 X 1 1 X 1 1 1 1 1 0 1 0 0 1 X^2 1 1 X^2+1 0 X^2+X+1 X 1 X^2+X 1 1 X^2+1 0 X 1 X^2+X+1 X^2 X 1 1 X^2+X+1 X^2+X X 1 0 1 0 X 1 X^2+1 0 X^2+X+1 X X^2 X^2+X+1 X^2+X 1 X^2+1 1 X^2+X+1 1 X^2+1 1 X X+1 X+1 X^2+1 1 X^2+X+1 1 1 1 X X 1 1 1 X+1 1 X^2+1 1 1 1 0 X+1 X^2+X 1 X^2+X X 0 1 1 X 1 X^2 1 X+1 X^2 1 X^2+X X^2+X X^2+X+1 X^2 0 0 0 1 0 X 0 X^2+X X 1 1 X+1 X^2+X+1 X+1 1 X^2+1 X^2+X X^2+X 1 X 1 X+1 X^2+X X+1 X^2+X X^2+1 X^2+X X^2+X X^2+X+1 X+1 1 X^2+X+1 X^2+X+1 1 0 X+1 1 0 1 X 1 X X^2 X^2+X+1 0 X^2 X^2+X X^2+X 1 X^2+1 0 X^2+1 X^2+1 1 X^2+1 X^2+X+1 X^2+X+1 0 1 1 X^2 X^2+X X^2+X X^2+X X 1 X^2 X^2+X+1 X^2+1 1 1 X^2+X+1 0 1 1 X X^2 X^2+X+1 X^2+X X X^2+1 1 X^2+X 1 X^2+X X+1 X^2 X X^2+1 0 0 0 0 1 X 1 X+1 X+1 X+1 X 0 1 X^2+1 X^2+X+1 X^2+X X X^2 0 X^2 X^2+X X^2+1 1 X^2+X+1 X^2+X+1 X^2+1 X^2+X+1 X^2+X+1 X^2+X X X+1 0 X^2+X+1 X^2+X+1 X^2+X 0 X^2 X^2 X^2+1 X+1 X+1 X^2 1 X^2+1 1 X^2+X X^2 X^2+1 X^2+X+1 X+1 X^2+1 X X 1 1 X 1 X^2+X+1 1 X^2+X X^2 X^2+X X^2 X^2+X X^2+1 X^2 X^2 X^2 X^2 1 X^2+X+1 X+1 X+1 X^2+1 X 0 X^2+X+1 1 1 X^2 X^2+X+1 X^2+X X 0 X+1 1 X+1 0 1 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+108x^81+344x^82+434x^83+660x^84+568x^85+706x^86+576x^87+627x^88+684x^89+572x^90+536x^91+536x^92+398x^93+409x^94+250x^95+247x^96+148x^97+144x^98+82x^99+61x^100+38x^101+31x^102+10x^103+11x^104+8x^105+2x^106+1x^108 The gray image is a linear code over GF(2) with n=356, k=13 and d=162. This code was found by Heurico 1.11 in 1.7 seconds.