The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  X  1  1  1  1  0  1  X  1  1  1  0  1  1  1  1  0  1  1  1  X  1
 0  1  1  0  1  1  0  1  1  X X+1  1  1  0 X+1  0 X+1  1 X+1  1  X  0 X+1  1 X+1  1  0 X+1  1  X  0  0  X  0
 0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  X  0  0  X  0  X  X  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  X
 0  0  0  0  X  0  0  0  0  0  X  X  X  X  0  X  X  X  X  X  0  X  X  X  0  0  X  X  0  0  X  0  0  0
 0  0  0  0  0  X  0  0  X  0  0  X  0  X  0  X  0  X  0  0  0  X  X  X  X  0  0  X  X  0  0  X  0  X
 0  0  0  0  0  0  X  0  X  X  0  0  X  X  0  0  X  0  X  0  X  X  X  X  0  0  0  0  X  0  0  X  X  0
 0  0  0  0  0  0  0  X  X  0  X  0  X  X  X  0  0  X  0  X  X  X  0  X  X  X  0  0  X  0  X  X  X  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+140x^28+98x^30+219x^32+138x^34+186x^36+134x^38+70x^40+14x^42+18x^44+6x^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 0.695 seconds.