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 X^2 X^2 X^2  0 X^2  1  X  0
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2+X X^2  0  X X^2+X  X  X X^2 X^2  0 X^2 X^2+X X^2+X  X X^2  X X^2  0  X X^2  X  X  0 X^2+X X^2  0
 0  0  X  0  0  0  X X^2+X  X  0  0  0  X  X  0  X X^2  0  X X^2  X  0 X^2+X X^2  X X^2 X^2+X  0  X  0 X^2+X  X  X X^2+X X^2  X  X  0  X
 0  0  0  X  0  X  X X^2+X  0  X  X X^2  0 X^2 X^2+X  X  X  X  X  0  0 X^2+X X^2+X  X  X  0 X^2 X^2+X  X  0 X^2 X^2+X X^2  0  0  X  0 X^2+X  0
 0  0  0  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2  X X^2 X^2+X X^2 X^2+X X^2+X  0  X  0  X X^2  0 X^2 X^2+X  X  X X^2+X X^2  0  0  0  X  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 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+204x^30+590x^32+881x^34+272x^35+1503x^36+976x^37+2961x^38+1568x^39+2972x^40+1056x^41+1547x^42+208x^43+882x^44+16x^45+506x^46+188x^48+43x^50+7x^52+1x^54+1x^58+1x^64

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 15.8 seconds.