The generator matrix

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

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+49x^26+78x^27+230x^28+232x^29+556x^30+508x^31+1035x^32+732x^33+1355x^34+720x^35+1088x^36+500x^37+556x^38+212x^39+192x^40+68x^41+35x^42+18x^43+10x^44+4x^45+8x^46+4x^48+1x^50

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 1.56 seconds.