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 X 0 X 0 X 1 1 0 X 0 1 1 X 1 1 1 1 0 X 1 1 0 X 0 1 0 1 1 1 X X 0 1 1 1 1 1 1 1 X 1 1 1 1 1 0 X^2 0 0 1 X^2 1 1 1 X^2 1 X^2 X 1 1 1 1 1 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X X^2 X^2+X 0 X^2+X X 0 X^2 0 0 X^2+X X^2+X X X 0 X^2 X^2+X X^2+X X X^2+X X X^2+X 0 0 X X^2+X X X^2+X X^2+X X^2+X 0 X 0 X^2 X X^2+X X^2+X 0 X X^2+X X X X X X^2 X^2 X^2+X X^2+X X X^2+X X X X^2+X 0 0 X X^2+X X^2+X X^2 0 X X^2+X X X X X X^2+X X 0 X^2+X X^2 X X^2+X X X X^2 0 X^2 X X^2+X 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 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 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 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 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 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 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 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 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 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 0 X^2 X^2 0 0 0 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 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 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 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 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 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+48x^82+8x^83+120x^84+38x^85+170x^86+100x^87+276x^88+174x^89+430x^90+406x^91+576x^92+800x^93+811x^94+1142x^95+1093x^96+1428x^97+1222x^98+1428x^99+1110x^100+1142x^101+824x^102+800x^103+553x^104+406x^105+373x^106+174x^107+213x^108+100x^109+132x^110+38x^111+92x^112+8x^113+48x^114+40x^116+24x^118+17x^120+7x^122+5x^124+6x^126+1x^142 The gray image is a linear code over GF(2) with n=392, k=14 and d=164. This code was found by Heurico 1.16 in 41 seconds.