The generator matrix

 1  0  0  0  1  1  1  0  1  X  1 X^2+X  1  1  0  1  X  1  X  X  X  1  1  1  0  1  1 X^2+X  0  X  1 X^2 X^2+X X^2  1  1  1  1  1
 0  1  0  0  0  1  1  1 X^2 X^2+X X^2+1  1  1  0  1 X+1  1 X^2+X  1 X^2 X^2+X  0 X^2+1  X  1  X X^2+1 X^2  1 X^2 X^2  X  X  1  1 X^2+1 X^2+X+1 X^2+X  0
 0  0  1  0  1  1 X^2 X^2+1 X^2+X+1  1  1 X^2+X+1 X^2 X^2+X X^2+X  1 X^2+1 X^2+1  0  1  X  0  0 X^2+1  X X^2+X X^2+X+1  1 X^2 X^2  X  1  1 X^2+X+1 X+1  0 X+1 X^2+X+1  0
 0  0  0  1  1  0 X^2+1  1 X^2  1 X^2+1 X^2  0 X^2+X+1 X^2+1 X^2+X X+1  1 X^2 X^2+X  1 X^2+X+1 X^2+X+1  X X^2+1 X^2 X^2 X^2+X+1  0  1 X+1 X+1  X  0  1  X  X X+1  0
 0  0  0  0  X  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2+X X^2+X  X  X  X X^2+X X^2+X  X X^2+X  X  X X^2+X X^2+X  X  X  X  X  X  0 X^2+X X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  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+108x^31+383x^32+868x^33+1291x^34+1824x^35+2578x^36+3300x^37+3881x^38+4094x^39+3996x^40+3436x^41+2683x^42+1894x^43+1210x^44+700x^45+294x^46+142x^47+56x^48+16x^49+10x^50+2x^51+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 21 seconds.