The generator matrix 1 0 0 0 1 1 1 X^2 1 1 0 1 1 0 X 1 X^2+X 1 1 X^2 X^2+X 1 1 X 1 1 X^2+X X^2 1 X^2+X X^2+X 1 X 1 1 1 X X^2+X X^2 X 1 X^2+X X^2 1 X^2 1 1 1 1 1 1 1 1 X^2 X^2 1 X^2+X X^2 X 1 1 1 X 0 1 1 1 0 0 X 1 0 X^2 1 1 0 1 1 1 1 X^2+X X^2+X X X^2+X 1 X^2 0 1 1 0 1 0 0 X X X^2+X 0 1 X^2+1 1 X^2+X+1 X+1 1 1 X^2+X 0 X+1 X^2 1 1 0 1 X^2 X+1 X^2+X X 1 1 1 1 X^2+X+1 1 0 X^2+X+1 X^2+1 X^2+X 1 X 1 0 X 1 X^2 X^2+X X X X^2+X+1 X^2+1 0 X+1 1 X^2+X+1 1 1 X^2+X+1 X 1 1 0 X X^2+X X^2 X^2 X^2+X+1 0 X+1 1 1 1 X^2+1 X 1 X+1 X^2 X X^2+1 0 X^2+X X^2+X+1 1 X^2 1 X^2 X^2+X+1 0 0 X^2+1 X^2 0 0 1 0 X X^2+X+1 X^2+X+1 1 X+1 0 X X 1 X^2+1 X^2+1 X^2 1 X+1 1 X+1 X X^2 X^2+X X X^2+1 1 1 0 X^2 1 1 X^2+X X+1 0 0 X^2+X+1 1 X^2+1 1 0 X^2+1 X^2 X^2+X 1 1 X X^2+1 X^2+X+1 X^2 X^2+X+1 X X^2+X 1 0 1 X^2+1 X^2+X X^2+X+1 X 0 0 X^2 1 X X X X^2 X^2+1 1 0 X 0 X+1 X^2+X+1 X^2+X+1 X^2 1 X^2+X 0 X^2 1 1 X^2+X X X^2+X 1 1 0 0 0 0 0 1 X+1 X^2+X+1 X 1 X X+1 X+1 X^2+X 1 X^2+1 X 0 X^2+X+1 X^2 X+1 0 X^2+X 1 0 1 X+1 X^2+X X X^2+1 X^2+1 1 X^2 X^2 X+1 X X^2+1 X^2+X X^2+1 X^2+X+1 X X^2 X+1 1 X X^2 X+1 X^2 0 X+1 0 X^2 1 X^2+X+1 X+1 X^2+X X^2+X 1 1 X^2+1 X^2+X+1 X^2 X^2 X 1 1 X^2+X+1 X 1 X^2 X^2+X+1 X^2 0 1 1 X X^2+1 1 X^2+1 X^2+X+1 X^2+X 0 X^2+X X^2+1 X^2+1 1 X X X+1 X^2+X X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 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+112x^81+360x^82+398x^83+679x^84+560x^85+678x^86+558x^87+733x^88+574x^89+653x^90+488x^91+616x^92+392x^93+363x^94+236x^95+269x^96+112x^97+162x^98+82x^99+69x^100+32x^101+18x^102+30x^103+1x^104+10x^105+5x^106+1x^110 The gray image is a linear code over GF(2) with n=356, k=13 and d=162. This code was found by Heurico 1.16 in 4.88 seconds.