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

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+28x^34+68x^35+52x^36+70x^37+102x^38+64x^39+49x^40+36x^41+9x^42+12x^43+10x^44+6x^45+4x^46+1x^66

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 0.0258 seconds.