The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  0 X^2+X  1 X^2  1  1  1  1  1  0  1  X  1  0  1  1  0 X^2+X  1  X X^2  X X^2  0  1  0 X^2+X X^2+X X^2+X  1
 0  1  0  0  1 X+1  1 X^2+X  X  1  1 X+1  X X+1 X^2+1 X^2 X^2+1 X^2+X+1  1 X^2+X+1 X^2+X X^2+X  1 X+1 X+1  1 X^2+X X^2+X  1  1  X X^2+X  1 X^2+1 X^2+X  1 X^2+X X^2  0
 0  0  1  1  1  0  1 X^2+1  X X^2+1 X^2+X  1  1  X X^2  1 X+1 X+1 X^2+X  0  1 X^2+1 X+1 X^2+X  1 X^2+1  1  0  0  X  1  1 X^2+X+1 X^2+X+1  1  X  1  1  0
 0  0  0  X  0  0 X^2 X^2  X X^2+X  X X^2+X X^2+X X^2 X^2+X  X X^2  X  X X^2+X X^2+X X^2 X^2+X X^2+X  X  X  X  0 X^2 X^2  0  0  0 X^2+X X^2+X X^2+X  0  0  0
 0  0  0  0  X X^2  X X^2+X X^2+X  0 X^2+X  0  X  X X^2 X^2+X X^2  X  0 X^2+X  0  0  X X^2  X  X  X  X X^2 X^2 X^2 X^2 X^2+X  0 X^2 X^2  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+64x^32+222x^33+335x^34+560x^35+749x^36+802x^37+929x^38+954x^39+921x^40+796x^41+700x^42+550x^43+288x^44+170x^45+71x^46+30x^47+24x^48+10x^49+11x^50+2x^51+1x^52+2x^54

The gray image is a linear code over GF(2) with n=156, k=13 and d=64.
This code was found by Heurico 1.16 in 1.75 seconds.