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  X  1  1  1  1  1  X  1
 0  X  0  X  0 X^2  X X^2+X  0 X^2  X X^2+X  0  0 X^2+X X^2+X  0 X^2 X^2+X  0 X^2+X X^2+X X^2 X^2+X X^2 X^2 X^2+X  X X^2  X  X  0 X^2+X X^2  0  X X^2+X X^2+X
 0  0  X  X  0  X X^2+X X^2  0  X  X  0  0 X^2+X  X X^2 X^2 X^2  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X  X  0 X^2  X X^2+X X^2  0  X X^2+X X^2 X^2  0
 0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  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+55x^34+71x^36+64x^37+147x^38+64x^39+54x^40+37x^42+17x^44+1x^46+1x^72

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 0.0323 seconds.