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

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+47x^34+16x^35+67x^36+48x^37+182x^38+48x^39+38x^40+16x^41+24x^42+20x^44+2x^46+1x^48+1x^50+1x^68

The gray image is a linear code over GF(2) with n=152, k=9 and d=68.
This code was found by Heurico 1.16 in 7.29 seconds.