The generator matrix

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

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+127x^28+160x^30+32x^31+345x^32+224x^33+318x^34+224x^35+316x^36+32x^37+134x^38+91x^40+26x^42+13x^44+2x^46+2x^48+1x^56

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 0.153 seconds.