The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  1  X  1  0  1 X^2+X  1 X^2+X  1  1 X^2+X  1 X^2  1 X^2+X  1  1 X^2+X  1  1  1  0  X  X  1 X^2  1  1  1  1  0  X X^2  1  1  1  X X^2 X^2  X  1  1 X^2 X^2+X  X  1  1  0  1 X^2  1 X^2  0  1  1  1 X^2+X  1 X^2  1  1  1  1 X^2+X  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  1  1  1 X^2  1  1 X^2+1  1 X^2+X X^2+X X+1  1  X  X X^2+X+1 X^2+X  1  X  1 X+1  1 X^2+X+1 X^2  0  0 X^2+X+1 X^2+X+1  0  1  1 X+1  1 X^2+1 X^2+X  1 X^2  1 X^2  1  X X^2 X^2+X  1  0  1  1 X^2+1  0  1  1  1 X^2+1 X+1 X^2+X  1  1 X^2+X  1  1  1 X^2 X^2+X+1  1  X X^2  0  1 X^2 X^2  1  1  1 X^2+X+1 X^2+X+1  X X^2 X^2 X^2+1  1 X^2+X+1  X
 0  0  1 X+1 X^2+X+1  0 X+1  X  1 X^2+1  X X^2+X X+1  1  X  0  X  1 X^2+X+1 X^2+1 X+1 X^2  X  0 X^2+1 X^2+X+1 X+1  1 X^2+1  1 X^2  1  X X^2+1  1 X+1 X^2+X  1 X^2+1 X^2  0  1 X+1 X^2+X X^2+X X^2+X+1 X+1  1  1  0 X+1  X X^2+X+1  0  X  0  X  1  0 X^2+X+1 X^2  0  1  X  X X^2+1 X^2+1  1  1  1 X+1  0 X^2 X^2 X+1 X^2+X X^2+X+1 X^2+1 X^2  0 X^2 X^2+X+1 X^2+X X^2+1  1
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0  0  0  0  0  0 X^2
 0  0  0  0 X^2  0 X^2  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  0  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 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  0  0
 0  0  0  0  0 X^2  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  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 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 78.

Homogenous weight enumerator: w(x)=1x^0+84x^78+190x^79+339x^80+402x^81+336x^82+414x^83+397x^84+290x^85+265x^86+280x^87+246x^88+178x^89+142x^90+154x^91+134x^92+60x^93+46x^94+46x^95+32x^96+24x^97+22x^98+4x^99+1x^100+6x^101+1x^102+2x^104

The gray image is a linear code over GF(2) with n=340, k=12 and d=156.
This code was found by Heurico 1.16 in 1.27 seconds.