The generator matrix

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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+185x^76+36x^77+418x^78+156x^79+771x^80+272x^81+818x^82+360x^83+965x^84+408x^85+932x^86+352x^87+827x^88+272x^89+616x^90+152x^91+339x^92+36x^93+126x^94+4x^95+73x^96+22x^98+28x^100+12x^102+7x^104+2x^108+1x^112+1x^116

The gray image is a linear code over GF(2) with n=340, k=13 and d=152.
This code was found by Heurico 1.16 in 6.9 seconds.