The generator matrix

 1  0  0  0  1  1  1  0 X^2  1  1  1  1  X  0 X^2+X  1  1 X^2+X  1  1  0  1  X  1 X^2+X  X  1  1 X^2+X  1  1  X  1
 0  1  0  0  0  1 X+1  1 X^2  X X^2+1 X^2+X+1  X  1  1  X X^2+X  0 X^2  1 X^2  1 X^2+X  1 X^2  1 X^2+X  X  X  1  X  X  1  0
 0  0  1  0  0  1 X^2+X+1  X  1 X+1 X^2+X X^2  1 X+1 X+1  1 X^2+X X+1  1 X^2 X+1 X^2+X+1 X^2+1  0 X^2+X X^2+X  0 X+1 X^2+X  1 X^2+X+1  X X^2+X X^2+X+1
 0  0  0  1  1 X^2 X^2+1  1 X+1  0 X^2+X  1 X+1  X X^2+X+1  0  1 X^2+X+1  1 X+1 X^2+X X^2+X+1 X^2 X+1 X^2  X  1 X^2+X  X  1  1 X^2 X+1 X^2+X+1
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 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+99x^28+380x^29+543x^30+710x^31+922x^32+968x^33+1006x^34+978x^35+927x^36+716x^37+442x^38+282x^39+125x^40+48x^41+22x^42+14x^43+6x^44+3x^46

The gray image is a linear code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.11 in 0.437 seconds.