The generator matrix

 1  0  0  1  1  1  X  1  1  0  1 X^2  1 X^2  1  1  0 X^2+X  1  X  1  1  0  1 X^2+X  1  1 X^2  1  1  X  1  1  1  1 X^2  0  X  1
 0  1  0  0  1 X^2+X+1  1 X^2 X^2+X+1  1  X X^2+X X^2+X+1  1  X X+1  1  0 X^2+1  1 X^2+1  X  0 X^2+X  1 X^2+1  X  1  1  1  1 X+1  X  X  1 X^2  1 X^2+X  0
 0  0  1  1 X+1  0  1 X^2+X+1  1  X  X  1  X X+1  1  X X^2  1 X^2+X X^2+X+1 X^2+X+1 X^2  1 X^2+1 X^2+1  X  1 X^2+X X^2+1 X^2+X+1 X+1  0 X^2+X+1  1 X^2  1 X^2+X  0  0
 0  0  0  X  X X^2+X X^2 X^2  0 X^2+X  X  X X^2  X  0 X^2+X  X X^2 X^2  0 X^2  0  X X^2+X  X X^2+X  X X^2+X  X  X X^2 X^2 X^2 X^2  0 X^2  0  X  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 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+98x^32+188x^33+384x^34+556x^35+665x^36+840x^37+895x^38+960x^39+963x^40+874x^41+636x^42+460x^43+299x^44+172x^45+125x^46+34x^47+22x^48+6x^49+7x^50+4x^51+2x^55+1x^58

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 1.71 seconds.