The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X^2 0 X X 1 X 0 X^2 X^2 1 X X 1 0 1 1 1 1 0 1 X 0 1 0 1 1 1 X 1 X 1 0 X 1 X^2 0 X 0 1 1 1 1 1 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2+X 0 0 X^2+X X X^2 0 0 X X X X 0 0 X X^2 X^2+X X X 0 X^2 X X^2+X X^2 0 X X 0 X X^2 0 0 X^2 X^2 X^2+X X^2 X 0 X^2 0 X^2+X X X^2+X X X^2 X^2+X X^2 X^2 X^2 X X^2+X X^2+X X X^2 0 X X^2+X X^2 X^2 X^2+X 0 0 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2+X X^2 X^2 X X X^2 X X^2+X 0 X X^2+X X^2+X X^2+X 0 X X^2+X X X X^2+X X 0 X X^2 X^2+X X^2 X 0 0 X^2 X^2+X X^2+X X^2+X X X X X^2+X X^2+X X X^2 X^2+X 0 0 0 0 X X^2 X 0 X^2+X 0 0 0 0 X^2+X 0 X^2+X X^2+X X^2+X X^2+X X 0 X 0 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X^2+X X 0 X 0 X X 0 0 X^2 X^2 X X^2 X^2 0 X X^2+X 0 0 X 0 X^2+X X^2 X^2+X 0 X^2+X X^2+X X^2+X 0 X^2 0 0 X^2+X 0 X^2 X^2+X X^2 X^2 X^2+X X X^2+X X^2+X 0 X^2+X X^2 0 X^2 X^2 X^2 0 X^2+X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 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 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 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 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 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 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+77x^72+74x^73+174x^74+242x^75+329x^76+382x^77+464x^78+574x^79+744x^80+968x^81+1087x^82+1202x^83+1289x^84+1318x^85+1273x^86+1262x^87+1013x^88+924x^89+751x^90+574x^91+447x^92+338x^93+218x^94+210x^95+149x^96+80x^97+84x^98+30x^99+39x^100+10x^101+33x^102+2x^103+8x^104+2x^105+6x^106+4x^110+1x^114+1x^122 The gray image is a linear code over GF(2) with n=340, k=14 and d=144. This code was found by Heurico 1.16 in 30 seconds.