The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 0 1 1 X^2+X 1 1 X 1 1 1 1 0 1 1 0 X^2+X 1 1 1 1 0 1 X^2+X 1 0 1 X^2 X^2+X 1 1 1 1 1 X^2+X 1 1 1 1 0 1 1 X^2 X^2+X 1 X^2 0 0 1 1 1 1 X 1 1 1 1 1 X^2 1 1 1 1 1 0 1 X 1 1 0 0 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 1 X^2+X X+1 1 X^2+1 0 1 X^2 X+1 X^2+X+1 X^2+X 1 X^2+1 0 1 1 X^2+X X^2+1 X^2+X X^2+1 1 X+1 1 0 1 0 1 1 X+1 X^2+X 0 1 X 1 X+1 X+1 X^2+X+1 0 1 X^2 X^2+1 1 1 X+1 1 1 1 0 X+1 X^2+1 X+1 1 X^2+X+1 0 X^2 X^2+X X^2+1 1 X^2 X^2 X^2+X+1 1 X+1 1 0 1 X^2+X X+1 1 1 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 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 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 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 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+112x^72+44x^73+148x^74+172x^75+452x^76+400x^77+432x^78+656x^79+625x^80+776x^81+632x^82+776x^83+606x^84+656x^85+432x^86+400x^87+385x^88+172x^89+148x^90+44x^91+73x^92+19x^96+16x^100+9x^104+5x^108+1x^112 The gray image is a linear code over GF(2) with n=328, k=13 and d=144. This code was found by Heurico 1.16 in 6.04 seconds.