The generator matrix

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

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+55x^32+64x^33+172x^34+298x^35+412x^36+442x^37+414x^38+484x^39+376x^40+438x^41+390x^42+220x^43+156x^44+70x^45+42x^46+20x^47+16x^48+10x^49+6x^50+2x^51+8x^52

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 0.445 seconds.