The generator matrix

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

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+51x^30+82x^31+180x^32+220x^33+241x^34+398x^35+598x^36+766x^37+992x^38+1136x^39+998x^40+862x^41+546x^42+352x^43+264x^44+170x^45+140x^46+78x^47+69x^48+30x^49+13x^50+2x^51+2x^52+1x^62

The gray image is a linear code over GF(2) with n=156, k=13 and d=60.
This code was found by Heurico 1.16 in 2.64 seconds.