The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+38x^30+89x^32+62x^34+16x^36+16x^38+18x^40+6x^42+4x^44+6x^46

The gray image is a linear code over GF(2) with n=68, k=8 and d=30.
This code was found by Heurico 1.16 in 0.016 seconds.