The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1  1 X^2+X X^2  1  X  1  1  1 X^2+X  1  1  1  1 X^2+X  1  1  X  0  1  1  X X^2  X  0  X  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X X^2+1  1  1 X^2+X  1  1  0  1 X+1 X^2  X  1  1 X^2+1 X^2+X X^2+X  1 X^2+X+1 X^2+X  1  0  1 X^2+X  1  1  1  1  0 X^2
 0  0  X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  0 X^2+X X^2+X X^2  0  X X^2 X^2+X X^2  X  X  0 X^2+X X^2  0  0 X^2  X  X  0  X  0  X  0 X^2+X X^2+X  0 X^2  X
 0  0  0 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 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+31x^32+118x^33+164x^34+192x^35+437x^36+286x^37+677x^38+338x^39+662x^40+332x^41+388x^42+158x^43+128x^44+88x^45+42x^46+14x^47+18x^48+6x^49+8x^50+2x^51+3x^52+2x^53+1x^54

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 0.45 seconds.