The generator matrix

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

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+299x^34+160x^35+549x^36+272x^37+809x^38+216x^39+611x^40+208x^41+455x^42+128x^43+239x^44+32x^45+91x^46+8x^47+8x^48+10x^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 1.16 in 98.4 seconds.