The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  X  1 X^2  1  1  0  1  X  1 X^2  1  1  X X^2  1 X^2+X  1  1  1  1 X^2  1 X^2  1  X  1  X  1 X^2  1  1  0 X^2+X  1 X^2  1 X^2+X  1  1  1  1  X  1  1  1  1  1  0  0  X  X  0  1  1 X^2+X X^2 X^2  1  X  1 X^2+X  1  X  1  1 X^2+X X^2+X X^2  1  1  1  1  X X^2
 0  1  0  0  1 X^2+X+1  1 X^2  0 X^2 X^2+X+1  1  1  1 X^2 X^2  1  1  1  1  X X+1 X^2+1 X^2+X  1  X  1 X^2+X X+1 X^2+X X^2  1 X^2+X+1  1  0  1  X X^2+X X^2+1  1 X+1  X  1 X^2  0 X^2 X^2+X+1 X^2+X  0 X+1  0 X^2+1  1 X^2+1  X X+1 X^2+X X^2+X  1  1  1  1  1 X+1 X^2+1  1  1 X^2  1  1  X  1 X^2+X  1 X^2 X^2+X+1  1 X^2+X X^2 X^2 X^2 X^2+1  1  0  1
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  0  1  0  1 X^2 X+1  1 X^2+X  1  1  X  1  1 X^2  0 X+1  X X^2+X+1 X+1 X^2+X X^2+1 X^2+X+1  X X^2+X+1  X  1  0 X^2+X X^2  1  0  1 X^2  1 X^2+X+1  1  1 X^2+X X^2  X  X X+1 X^2+X  X X^2+1 X^2+1 X^2+1 X^2+X+1 X^2+1 X^2 X+1 X+1  0 X^2 X^2  1 X^2+X+1 X^2+X X^2+1 X+1  0 X^2+X X^2+1  1 X^2+X  1  1 X^2 X^2+1  1  0  1 X^2+X+1
 0  0  0  X  X X^2+X X^2 X^2+X  0  0  X X^2 X^2+X  0  X X^2  X  0  X X^2  X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X  X  0 X^2 X^2 X^2 X^2+X  X  X X^2+X  0 X^2+X X^2+X X^2  0  X  X  0 X^2+X  X X^2  0  X X^2+X  0 X^2  0 X^2  0  X X^2  X X^2+X  0 X^2  0  0  0  0 X^2 X^2+X X^2+X X^2+X X^2+X  X  0 X^2+X X^2 X^2+X X^2 X^2+X  0  X X^2  0  0 X^2 X^2+X X^2+X
 0  0  0  0 X^2  0  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 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2  0  0  0  0  0  0  0  0  0  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 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+124x^77+320x^78+458x^79+531x^80+590x^81+635x^82+652x^83+680x^84+684x^85+677x^86+550x^87+436x^88+478x^89+372x^90+288x^91+258x^92+130x^93+120x^94+82x^95+40x^96+36x^97+13x^98+12x^99+6x^100+6x^101+3x^102+6x^103+4x^106

The gray image is a linear code over GF(2) with n=340, k=13 and d=154.
This code was found by Heurico 1.16 in 6.47 seconds.