The generator matrix

 1  0  0  1  1  1  X X^2+X  1  1 X^2  1  1 X^2+X  1  1 X^2  1  X  1  X  1  1  X X^2+X  1  X X^2  1  1  1  1  X  1 X^2+X X^2+X X^2 X^2+X
 0  1  0  0 X^2+1 X+1  1  0 X^2 X+1  1  1  0  1 X^2+X+1 X^2+X+1 X^2  X  1 X^2  1  X X^2+1  1  1 X^2+X  0  1  1 X^2+X X^2  X  1  0 X^2+X X^2+X X^2+X  0
 0  0  1  1 X^2+1 X^2 X^2+1  1  0 X+1  1  0 X^2+X+1 X^2 X+1 X^2  1  1 X^2+X X^2+X X^2+X+1 X^2  1 X^2 X^2+X+1 X^2+X+1  1  X X^2  X X^2+X+1 X+1  X X^2+X  1  1  1  1
 0  0  0  X  X  0  X X^2+X  X X^2  0 X^2+X X^2 X^2+X  0 X^2+X X^2+X X^2 X^2+X X^2  0  X X^2+X X^2  X  X  0 X^2 X^2  0 X^2+X  0 X^2  X  X  0 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+248x^34+148x^35+435x^36+144x^37+318x^38+80x^39+271x^40+104x^41+148x^42+28x^43+85x^44+8x^45+22x^46+8x^48

The gray image is a linear code over GF(2) with n=152, k=11 and d=68.
This code was found by Heurico 1.16 in 37.9 seconds.