The generator matrix

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

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+144x^32+310x^34+64x^35+501x^36+256x^37+614x^38+384x^39+626x^40+256x^41+426x^42+64x^43+267x^44+114x^46+53x^48+8x^50+7x^52+1x^60

The gray image is a linear code over GF(2) with n=156, k=12 and d=64.
This code was found by Heurico 1.16 in 0.978 seconds.