The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+85x^28+24x^29+248x^30+88x^31+317x^32+144x^33+310x^34+144x^35+277x^36+88x^37+172x^38+24x^39+65x^40+38x^42+22x^44+1x^48

The gray image is a linear code over GF(2) with n=136, k=11 and d=56.
This code was found by Heurico 1.16 in 0.137 seconds.