The generator matrix

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

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+64x^31+426x^32+844x^33+1295x^34+1956x^35+2399x^36+3482x^37+3698x^38+4172x^39+3838x^40+3590x^41+2719x^42+2016x^43+1145x^44+584x^45+272x^46+148x^47+61x^48+26x^49+12x^50+12x^51+2x^52+2x^53+4x^54

The gray image is a linear code over GF(2) with n=156, k=15 and d=62.
This code was found by Heurico 1.13 in 6.98 seconds.