The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  X  1  1 X^2  1  1  1  X  X  1  1  1  1  1  1  1 X^2 X^2  1  1  1  1  1 X^2  1  1  X  1  1  1
 0  1  1 X^2+X X^2+X+1  1 X^2 X+1  1  1  X X^2+1  1  1  0 X^2+X+1  1  1 X^2+X+1 X^2  X X+1 X^2 X^2+X+1  0  1  1 X^2+1  X X^2+1 X^2+1 X+1  1 X+1 X^2+1  1  0  1 X+1
 0  0  X  0 X^2+X  0  X X^2 X^2+X X^2+X  X X^2  X  X  0  X X^2 X^2+X X^2 X^2+X X^2+X  0 X^2  X X^2+X  X  0 X^2+X  X  0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X X^2 X^2+X  0
 0  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  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  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  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+125x^34+96x^35+263x^36+192x^37+275x^38+192x^39+269x^40+192x^41+218x^42+96x^43+93x^44+16x^46+8x^48+5x^50+4x^52+1x^54+2x^56

The gray image is a linear code over GF(2) with n=156, k=11 and d=68.
This code was found by Heurico 1.16 in 0.137 seconds.