The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+62x^25+426x^26+1222x^27+2352x^28+4154x^29+6978x^30+10198x^31+13811x^32+17168x^33+18095x^34+16886x^35+14382x^36+10692x^37+6889x^38+3866x^39+2080x^40+1130x^41+471x^42+148x^43+46x^44+10x^45+5x^46

The gray image is a linear code over GF(2) with n=136, k=17 and d=50.
This code was found by Heurico 1.13 in 82.3 seconds.