The generator matrix

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

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+40x^34+198x^35+202x^36+306x^37+176x^38+378x^39+153x^40+198x^41+109x^42+114x^43+58x^44+70x^45+10x^46+14x^47+16x^48+2x^49+1x^50+2x^52

The gray image is a linear code over GF(2) with n=156, k=11 and d=68.
This code was found by Heurico 1.11 in 0.063 seconds.