The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 X 1 X^2 1 1 1 1 0 1 1 X^2+X 1 1 X^2+X 1 1 X^2 X 1 1 1 0 0 1 1 1 X^2+X 1 1 1 X^2+X 1 1 X 1 1 X^2+X X^2 1 1 1 X^2 1 X 1 0 X 1 1 1 1 1 1 1 1 0 1 1 1 1 X^2 1 0 1 X X 1 1 1 1 X^2+X 1 1 0 1 0 1 X 0 1 1 0 1 X^2 1 1 1 X 0 1 1 X^2+X X^2+X+1 1 0 X+1 1 X 1 X^2+1 1 0 X^2+X+1 X^2 X^2+X+1 1 X^2+X 1 1 X^2+X 1 1 0 X^2+X 1 1 X+1 X^2+1 X+1 1 1 X^2+1 0 X^2+X 1 X^2+X+1 X^2 1 1 0 X^2+X 1 X^2+1 X^2+X 1 1 0 X+1 1 1 X^2+X+1 1 X^2+X 1 1 X+1 X X^2 1 X^2+X+1 X^2+X+1 0 X^2 1 X^2 1 0 1 1 0 X^2 1 1 1 1 X^2+X X X^2 1 X^2 X^2+X+1 X^2 X^2+X+1 1 X^2+X 1 X X X^2+X 0 1 1 0 X^2 X^2+X 0 0 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X X^2 X X^2 X X X^2 X^2 X X^2+X X^2 X^2 0 X^2+X 0 0 X X 0 X^2 0 0 0 X^2 0 0 X^2 X X X 0 0 X^2+X X X 0 X^2 0 X^2+X X^2 X X X^2 X 0 X^2+X X^2 X^2+X X X^2+X X X X^2+X 0 X^2 X X^2 X^2+X X 0 0 X^2 X X^2 X^2 0 X 0 X^2 X^2+X 0 X X X 0 X X^2 X X^2+X X^2 0 X X X X X^2+X X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 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 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 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 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 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 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 X^2 0 0 0 0 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 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 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 0 0 X^2 0 0 0 X^2 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 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+111x^86+12x^87+288x^88+136x^89+582x^90+348x^91+873x^92+636x^93+1121x^94+924x^95+1504x^96+1024x^97+1600x^98+1032x^99+1345x^100+904x^101+1055x^102+628x^103+767x^104+344x^105+466x^106+124x^107+248x^108+28x^109+133x^110+4x^111+74x^112+36x^114+13x^116+10x^118+3x^120+4x^122+1x^124+2x^126+3x^128 The gray image is a linear code over GF(2) with n=392, k=14 and d=172. This code was found by Heurico 1.16 in 26.7 seconds.