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^2 1 1 0 1 X^2+X X 1 1 1 1 1 0 1 1 1 0 X^2+X 1 1 X X^2+X 1 1 1 1 X 1 1 X^2+X 1 X X^2 1 1 1 1 X^2+X 0 1 1 X X 1 1 1 1 1 X 0 X^2 1 X^2+X 1 1 X^2 1 0 0 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 0 1 1 X+1 X+1 1 X^2+1 1 1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X+1 1 1 X X^2 1 1 X^2+X X^2 1 1 X^2+X+1 1 X^2+X X^2+1 1 X X^2 1 X^2+1 1 1 1 X^2+1 X^2+X+1 X+1 1 1 1 X+1 1 1 0 X+1 X^2 X^2+X+1 X^2+X 1 1 X^2 X^2+X 1 0 X^2 1 X^2+X+1 X X X^2 0 X^2 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 0 0 X^2 X^2 X^2 X 0 X^2 X X X^2 X X X^2+X 0 X^2 X^2 X^2 X X^2 X X^2+X X^2 X^2+X X^2+X X 0 0 0 X^2+X X^2+X X X X^2+X X^2+X X X^2 0 0 X^2 0 0 X^2 X^2+X X^2+X X^2+X X^2 X^2+X X 0 0 0 0 X 0 X^2+X X^2+X X 0 X 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 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 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 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 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 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 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 X^2 0 0 X^2 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 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 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 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 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 0 X^2 X^2 X^2 0 0 X^2 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 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+32x^77+101x^78+140x^79+304x^80+386x^81+438x^82+628x^83+799x^84+1026x^85+1186x^86+1212x^87+1261x^88+1356x^89+1344x^90+1326x^91+1197x^92+914x^93+798x^94+640x^95+407x^96+318x^97+175x^98+124x^99+92x^100+42x^101+35x^102+24x^103+21x^104+20x^105+10x^106+2x^107+5x^108+2x^109+7x^110+6x^112+1x^114+3x^116+1x^118 The gray image is a linear code over GF(2) with n=356, k=14 and d=154. This code was found by Heurico 1.16 in 35.7 seconds.