The generator matrix

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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+252x^79+270x^80+480x^81+342x^82+524x^83+309x^84+410x^85+160x^86+292x^87+164x^88+242x^89+128x^90+164x^91+94x^92+82x^93+16x^94+64x^95+21x^96+30x^97+18x^98+16x^99+5x^100+4x^101+8x^102

The gray image is a linear code over GF(2) with n=340, k=12 and d=158.
This code was found by Heurico 1.16 in 3.25 seconds.