The generator matrix

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

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+51x^28+146x^29+320x^30+330x^31+491x^32+380x^33+612x^34+524x^35+472x^36+282x^37+272x^38+102x^39+66x^40+24x^41+12x^42+5x^44+4x^47+2x^48

The gray image is a linear code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 0.302 seconds.