The generator matrix

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

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+86x^28+170x^30+231x^32+146x^34+150x^36+94x^38+94x^40+38x^42+12x^44+2x^48

The gray image is a linear code over GF(2) with n=68, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0674 seconds.