The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+138x^26+411x^28+56x^29+664x^30+256x^31+1153x^32+728x^33+1418x^34+704x^35+1160x^36+232x^37+710x^38+64x^39+314x^40+8x^41+132x^42+29x^44+10x^46+4x^48

The gray image is a linear code over GF(2) with n=136, k=13 and d=52.
This code was found by Heurico 1.16 in 2.15 seconds.