The generator matrix

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

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+292x^31+863x^32+1568x^33+2636x^34+3466x^35+5214x^36+6316x^37+8040x^38+8128x^39+8384x^40+6752x^41+5383x^42+3692x^43+2466x^44+1212x^45+628x^46+252x^47+148x^48+56x^49+16x^50+10x^51+12x^52+1x^58

The gray image is a linear code over GF(2) with n=156, k=16 and d=62.
This code was found by Heurico 1.13 in 28.5 seconds.