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

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+41x^30+74x^31+181x^32+248x^33+378x^34+468x^35+558x^36+780x^37+910x^38+956x^39+881x^40+788x^41+584x^42+488x^43+352x^44+212x^45+113x^46+58x^47+64x^48+20x^49+22x^50+4x^51+10x^52+1x^56

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 2.58 seconds.