The generator matrix

 1  0  0  0  1  1  1 X^2  1 X^2+X  1 X^2+X  0  1  1  1  1  1  X  1  X  0 X^2 X^2+X X^2  X  1  1  1  1  1  0  1  1
 0  1  0  0  0  1  1  1 X^2+X  1 X^2+X  1  0 X^2+X+1 X+1 X^2 X^2 X^2+1  1  X X^2  X  0  1  1  1 X+1  X X^2+X+1 X+1 X^2+X+1  1 X^2  0
 0  0  1  0  1  1  0  1 X^2  0  1 X^2+X+1  1 X^2+X X^2+1 X^2+X X^2+X+1 X^2+1 X^2 X^2+X  1  X  1  0 X^2+1  1  0 X^2+X+1 X^2+X+1 X^2+X X^2+X+1 X+1  X  0
 0  0  0  1  1  0  1 X+1 X^2+X+1 X+1  X  X X+1 X^2  1  X X^2+X X^2+X X^2+1 X^2+X+1  X  1 X+1 X^2  1  0 X^2+X+1  X  1  1 X^2+X+1  1 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  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+98x^26+312x^27+585x^28+1414x^29+1613x^30+2904x^31+3000x^32+4470x^33+3713x^34+4684x^35+3113x^36+3142x^37+1526x^38+1152x^39+572x^40+314x^41+84x^42+36x^43+21x^44+4x^45+5x^46+3x^48+1x^50+1x^52

The gray image is a linear code over GF(2) with n=136, k=15 and d=52.
This code was found by Heurico 1.16 in 16.1 seconds.