The generator matrix

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

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+112x^76+52x^77+437x^78+268x^79+592x^80+416x^81+740x^82+520x^83+805x^84+584x^85+773x^86+496x^87+645x^88+416x^89+455x^90+248x^91+305x^92+68x^93+112x^94+4x^95+57x^96+23x^98+28x^100+18x^102+11x^104+2x^106+2x^108+1x^112+1x^120

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 5.96 seconds.