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 1 1 1 1 0 X X X 0 X^2 0 X X 1 0 0 X X^2 1 1 X X 1 X X^2 1 1 0 X X 1 1 1 0 X^2 1 0 1 X 0 1 X^2 0 X 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 X^2+X X^2+X 0 X 0 X^2+X 0 X^2 X^2 X^2 X X X X 0 X^2 X 0 0 X^2 X X^2+X X^2+X X^2 0 X X^2 X X^2 X^2+X X^2+X 0 X^2 X^2 X^2+X X^2+X X^2 X X X^2 X^2 X X X^2+X X X X^2 X^2 0 X X X^2 0 X^2+X X^2+X X^2+X X^2 X^2 0 X^2 X X^2 X X^2 X X^2 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 X^2 0 X^2 X X^2 X^2+X X^2 X^2+X X X X^2 X^2+X 0 0 X^2 X^2 0 X^2+X X 0 X 0 X^2+X X X^2+X 0 X X X^2 X^2+X X^2+X X^2 X X X X^2+X X^2+X X^2+X X^2 X^2+X 0 X^2+X X^2+X X^2 X X^2 0 X X^2+X X 0 X^2+X X X^2 X X X 0 X X 0 X^2+X X^2+X X 0 X X 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 X X X^2 X^2 X^2 X X X^2+X X^2+X X^2 0 0 X^2 X^2+X X^2 X^2 0 0 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X 0 X^2+X X^2+X X^2+X X^2+X X X X X^2 X X^2+X X^2+X X X^2+X X^2+X X X 0 0 0 X^2+X X X 0 X^2 X 0 X^2+X X^2+X X X^2 X^2+X X X^2+X X^2 X 0 0 0 0 0 X^2+X 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 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 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 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 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+230x^72+8x^73+428x^74+60x^75+781x^76+132x^77+962x^78+408x^79+1242x^80+620x^81+1816x^82+800x^83+1529x^84+816x^85+1782x^86+664x^87+1184x^88+424x^89+972x^90+100x^91+643x^92+44x^93+350x^94+16x^95+223x^96+4x^97+80x^98+35x^100+10x^102+14x^104+4x^108+2x^112 The gray image is a linear code over GF(2) with n=336, k=14 and d=144. This code was found by Heurico 1.16 in 30.3 seconds.