The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1 X^2+X  1  1  0  1  1 X^2+X  0  1  1  1  1  1  X  1 X^2  1  1  0 X^2  1 X^2+X  1  1  1  1  1  1  X  1  1  1  1  1 X^2 X^2+X  X X^2  0 X^2 X^2+X  X X^2+X X^2 X^2  1 X^2+X X^2+X X^2 X^2  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  0  1  X  1  0  1  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1 X^2+X  1 X^2+X X+1  1 X+1  0  1  1 X^2+1 X^2+1 X^2 X^2+X+1  0  1 X^2+X+1  1  1  0  1  1 X^2+1  1  X  1  1  0 X+1 X^2  1 X^2+X+1  0 X^2+1  0  X  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1 X^2+X X^2+1  X X+1  1  1 X^2+X  X X^2+X  0 X^2+X+1  X X^2+1  X X^2+X  X X^2+X+1 X^2 X^2+X+1  1  X X^2+X
 0  0  X  0 X^2+X  0 X^2+X X^2  X  X  X X^2  0  0 X^2+X  0 X^2 X^2+X X^2 X^2+X  X  0 X^2+X X^2+X X^2 X^2+X  X X^2+X X^2+X X^2+X X^2 X^2 X^2 X^2  0 X^2+X  0 X^2+X X^2  0  X X^2 X^2+X X^2  X  0 X^2+X  X X^2+X X^2+X  X  0  0  0  0 X^2+X X^2  X  0 X^2  0  0 X^2+X X^2 X^2  0  X X^2+X X^2+X  X  0 X^2  0 X^2  X  X  X X^2+X X^2 X^2 X^2  0 X^2  0 X^2+X
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  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  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 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 X^2 X^2  0  0  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  0  0  0
 0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  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 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  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 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 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 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  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+78x^77+125x^78+256x^79+207x^80+362x^81+251x^82+402x^83+230x^84+430x^85+185x^86+380x^87+242x^88+340x^89+166x^90+212x^91+67x^92+50x^93+26x^94+16x^95+13x^96+18x^97+10x^98+10x^99+3x^100+2x^101+1x^102+4x^103+5x^104+1x^106+2x^110+1x^118

The gray image is a linear code over GF(2) with n=340, k=12 and d=154.
This code was found by Heurico 1.16 in 18.8 seconds.