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  1  1  1  1  X  1  1  1  1  X X^2
 0  X  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2+X  X  X  X X^2+X  X  X X^2+X X^2+X X^2+X X^2 X^2+X  X X^2+X  0  X  X
 0  0  X  0  0  0  0  0  0  0  X X^2+X  X X^2+X X^2+X  X X^2+X  0 X^2 X^2  0 X^2+X  X X^2+X  X X^2  0  X  X  0 X^2 X^2 X^2  X X^2+X  X X^2  X  0
 0  0  0  X  0  0  0  X X^2+X  X  X  X  0 X^2+X  0 X^2+X X^2  X  X X^2 X^2  0 X^2  X X^2  0 X^2 X^2 X^2+X  0  X X^2  X X^2+X  X  X  X  X X^2+X
 0  0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2+X  X X^2+X  X  X X^2+X  X X^2 X^2 X^2 X^2 X^2+X  X  0 X^2  0 X^2 X^2+X X^2 X^2+X X^2+X X^2+X  X  0  0 X^2
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  X  0 X^2  X  0  X X^2+X  0 X^2 X^2+X  0  0  0 X^2 X^2  0  0 X^2 X^2+X X^2 X^2+X X^2+X X^2 X^2+X  X  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0  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+200x^30+568x^32+888x^34+1309x^36+768x^37+3155x^38+2560x^39+3218x^40+768x^41+1323x^42+883x^44+537x^46+160x^48+41x^50+4x^52+1x^72

The gray image is a linear code over GF(2) with n=156, k=14 and d=60.
This code was found by Heurico 1.16 in 11 seconds.