The generator matrix

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

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+201x^34+296x^35+464x^36+484x^37+589x^38+402x^39+430x^40+266x^41+349x^42+244x^43+176x^44+80x^45+91x^46+18x^47+1x^48+2x^49+2x^50

The gray image is a linear code over GF(2) with n=156, k=12 and d=68.
This code was found by Heurico 1.11 in 0.14 seconds.