The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  1  0  1  1  0  1  X  1  1  1  1  0  1  X  1  1  1  X  X  1
 0  1  1  0  1  1  0 X+1  1  1  0  1 X+1  0 X+1  1 X+1  0  1  X  1  0  X  X X+1  1 X+1  1 X+1 X+1  X  X  0  0
 0  0  X  0  0  0  0  0  0  X  X  X  0  0  X  X  X  X  0  X  X  0  X  X  0  0  0  X  X  0  0  0  0  0
 0  0  0  X  0  0  0  X  0  X  X  0  0  X  0  X  0  X  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0
 0  0  0  0  X  0  0  0  X  X  0  X  X  X  X  0  X  0  0  0  0  0  0  X  X  0  X  0  X  0  X  X  0  X
 0  0  0  0  0  X  0  X  X  X  0  0  0  0  X  0  X  X  0  X  X  X  X  0  X  0  X  0  0  0  0  X  0  X
 0  0  0  0  0  0  X  X  0  X  0  X  X  0  X  X  0  0  X  X  0  X  X  X  X  X  X  0  X  0  0  0  0  0

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+29x^28+38x^29+46x^30+48x^31+36x^32+46x^33+48x^34+48x^35+32x^36+34x^37+24x^38+32x^39+24x^40+10x^41+8x^42+3x^44+2x^46+3x^48

The gray image is a linear code over GF(2) with n=68, k=9 and d=28.
This code was found by Heurico 1.16 in 0.016 seconds.