The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 X^2+X 1 1 0 1 1 1 0 1 1 X^2+X 1 1 0 1 X^2+X 1 1 1 1 1 0 1 X^2+X 1 1 0 1 X^2 X^2+X 1 1 1 X^2+X 0 1 1 1 1 1 1 X^2+X X 1 1 X^2+X 1 1 1 X X 0 1 X 1 1 1 1 0 1 1 X^2+X 1 X^2+X X^2+X 1 1 1 1 0 0 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 X^2+X 1 X+1 0 1 X^2+1 0 X^2+1 1 X^2+X X+1 1 X+1 X^2+1 1 0 1 X^2+X X^2+1 0 X+1 X^2+X 1 X 1 X^2+1 0 1 X^2 1 1 X+1 X^2+X X^2+1 1 1 X+1 X^2+1 X^2+X 0 X+1 X^2+X 1 1 X^2+1 X+1 1 0 X^2+1 1 1 1 1 1 1 1 X^2 X^2+1 0 1 0 X^2+1 1 X^2 1 1 X^2+1 X^2+X+1 0 X^2+X 1 1 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 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 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 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 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 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 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+65x^72+44x^74+24x^75+267x^76+208x^77+200x^78+544x^79+450x^80+1192x^81+308x^82+1728x^83+555x^84+2448x^85+432x^86+2448x^87+527x^88+1728x^89+308x^90+1192x^91+355x^92+544x^93+200x^94+208x^95+213x^96+24x^97+44x^98+68x^100+34x^104+16x^108+6x^112+3x^116 The gray image is a linear code over GF(2) with n=344, k=14 and d=144. This code was found by Heurico 1.16 in 22.5 seconds.