The generator matrix

 1  0  0  1  1  1  0  1  1 X^2 X^2  0  1  X  1  X  1 X^2+X  1  X  1  1  1  1 X^2+X X^2  1  1  1  X  1  0  1  1
 0  1  0  0  1  1  1 X^2  0  X  1  1 X+1  X  1  1  X  1  X  1 X+1 X^2+X+1 X^2+X+1 X^2+X+1  0  1  0  0  X  1 X^2+X X^2 X^2+1  X
 0  0  1 X+1 X^2+X+1  0 X+1  X X^2+1  1  1 X^2+X X+1  1  X  1 X^2+1 X^2+X+1 X^2+X X^2  0  1  X  1  1  0 X+1  0 X^2+X+1  X  0  1  1 X^2+1
 0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 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+214x^28+220x^29+568x^30+528x^31+1208x^32+796x^33+1230x^34+800x^35+1114x^36+500x^37+542x^38+208x^39+196x^40+20x^41+26x^42+16x^44+2x^46+3x^48

The gray image is a linear code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.16 in 1.28 seconds.