The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 0 1 1 1 X^2+X 1 1 X 1 1 1 0 1 1 0 1 1 X^2+X X^2 1 1 1 1 0 X^2+X 1 X^2+X 1 1 0 1 X^2+X 1 1 1 0 1 1 1 X^2+X 1 1 1 X^2 1 1 1 1 1 1 1 X^2+X 1 1 1 1 1 1 1 X^2+X 1 1 1 1 1 X^2 X^2 1 0 1 1 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 1 0 X^2+1 X^2+X 1 X+1 X^2+X+1 1 X 0 X^2+1 1 X^2+1 X^2 1 X+1 X^2+X 1 1 X+1 X^2+X 0 X^2+1 1 1 X^2+1 1 X^2+X X+1 1 X^2+X+1 1 X^2+X 0 X^2+1 1 0 X^2+1 X+1 1 X+1 X^2+1 1 1 0 X X+1 1 X^2+X 0 1 1 X^2+1 X X^2+X X X+1 1 X^2+1 1 X X X^2+X+1 X^2 1 1 1 0 1 X^2+X X^2+X X^2+X 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 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 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 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 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 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 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 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 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 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 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 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 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+29x^74+40x^75+140x^76+112x^77+326x^78+192x^79+578x^80+240x^81+886x^82+280x^83+1154x^84+320x^85+1156x^86+280x^87+854x^88+240x^89+552x^90+192x^91+289x^92+112x^93+93x^94+40x^95+30x^96+16x^98+12x^100+6x^102+8x^104+4x^106+5x^108+3x^110+1x^112+1x^122 The gray image is a linear code over GF(2) with n=340, k=13 and d=148. This code was found by Heurico 1.16 in 6.22 seconds.