The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X X^2+X  1 X^2  1 X^2+X  0  0  1  1  1  1 X^2  1  1  0 X^2  1 X^2+X  0  1  1  1  X  1  X X^2  1
 0  1  0  0  0  1  1  1 X^2+X+1 X^2+1  X  1 X^2+X X^2  1  0  1  1  1 X+1 X^2+1 X^2+X  1 X^2  0 X+1  X  1  1  X  1 X^2 X^2+X+1 X^2+X+1  1 X^2+1  0  1 X^2+X
 0  0  1  0  1  1  0  1 X^2+1 X^2+X  X X^2+1  1  1  0  X  1 X^2+X X+1 X+1  0 X^2  0  1 X+1 X^2+1  1  0 X+1  X X^2+1  X X^2  X X+1  0  1 X^2+X+1 X^2+X
 0  0  0  1  1  0  1 X^2+1 X^2+X+1 X^2 X^2+X+1  0 X+1  0 X^2+1  X  X X^2 X+1 X^2+X+1  X X+1 X^2+X+1  1  0  0  X X^2+X X^2+X+1  1 X+1  X X^2+1 X+1  X  0 X^2 X^2  1
 0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0  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+90x^31+406x^32+754x^33+1346x^34+1814x^35+2892x^36+3176x^37+3879x^38+3708x^39+4308x^40+3144x^41+3024x^42+1936x^43+1154x^44+576x^45+311x^46+130x^47+69x^48+30x^49+14x^50+2x^51+2x^52+1x^54+1x^62

The gray image is a linear code over GF(2) with n=156, k=15 and d=62.
This code was found by Heurico 1.16 in 20.5 seconds.