The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 1 X 1 1 X X 1 1 0 1 1 0 1 1 X^2+X 1 1 1 1 1 X^2 1 X^2+X 1 1 1 1 X^2 1 1 1 X X^2 1 X X^2 1 1 X 1 1 1 1 1 1 1 1 X^2+X X^2+X X^2 1 1 X X^2 X^2 0 1 X^2 X 1 1 1 1 1 1 1 1 1 X^2 1 0 1 1 0 X^2+X+1 1 X+1 X^2+X 1 X^2 X^2+1 1 X X^2+X+1 1 1 1 X^2+X 1 1 X 1 0 X+1 1 X^2+X 1 X^2 X+1 X^2+1 1 X+1 1 X 1 0 X^2+X+1 1 X 1 X^2 1 1 X 1 1 X^2+X+1 X^2 1 1 X^2+1 0 X^2+X+1 X^2 1 X 0 1 1 1 X+1 X^2 0 1 1 1 X^2+X 1 X^2+X 1 0 X^2+X X+1 X^2+X+1 X^2+X X^2+X+1 X+1 X^2 X 0 0 0 X 0 X^2+X 0 X^2 X^2 X X^2+X 0 X^2+X X^2+X X^2 0 X X^2+X X^2+X X^2+X X^2 0 0 X X^2+X X^2+X 0 X^2 X^2+X X^2 0 X^2+X X^2 X^2 X X 0 X 0 X X^2 0 0 0 X X^2+X 0 X^2+X 0 X^2+X X X^2 X X^2+X 0 0 X X X X^2 X^2+X X^2+X X X^2 0 X^2 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2 X X^2 X^2 0 0 0 0 X 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2+X X^2+X X X^2+X X^2+X X X^2+X X^2+X X X^2+X X^2+X X^2+X X^2 X X^2 X^2+X 0 0 0 0 X X^2 X^2 X^2+X X^2+X 0 X^2 X^2+X X X^2+X X^2+X 0 0 X 0 0 X 0 X^2+X 0 0 X^2 X^2 X X^2+X X^2+X X^2 0 X^2+X X 0 X X^2+X 0 X^2+X X^2 X^2 X X^2+X X X^2 X^2 0 0 X^2+X X^2+X 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 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 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+52x^72+160x^73+151x^74+322x^75+256x^76+394x^77+253x^78+490x^79+211x^80+362x^81+224x^82+388x^83+187x^84+248x^85+102x^86+124x^87+42x^88+44x^89+17x^90+14x^91+10x^92+6x^93+14x^94+2x^95+6x^96+2x^97+3x^98+4x^99+3x^100+3x^102+1x^106 The gray image is a linear code over GF(2) with n=320, k=12 and d=144. This code was found by Heurico 1.16 in 1.39 seconds.