The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  X  1  X  X X^2  1  1  0  X  1  1  X  X  1
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X X^2 X^2  0 X^2+X  0 X^2+X  X  X  X X^2+X X^2+X  X  X  X  X X^2  X X^2 X^2+X  0  0  0  X  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2  X  X  X X^2  0  0  0 X^2 X^2  0  0 X^2+X  X  X X^2+X X^2 X^2  X  0 X^2+X X^2+X X^2+X  0  0
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  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+172x^32+16x^33+268x^34+96x^35+466x^36+240x^37+650x^38+320x^39+698x^40+240x^41+370x^42+96x^43+262x^44+16x^45+110x^46+55x^48+10x^50+8x^52+2x^56

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 1.4 seconds.