The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  X  1  X  X  X  X
 0  X  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  0  0  0  X  X  0  X  X  0  0  X  X  X  X  0  X  0
 0  0  X  0  0  0  0  X  0  0  X  X  0  X  X  0  0  X  0  X  X  X  0  0  0  X  X  X  0  X  0  0  0  X
 0  0  0  X  0  0  0  X  0  X  X  0  0  X  0  X  0  0  0  0  X  X  X  X  X  0  X  0  X  0  0  X  0  X
 0  0  0  0  X  0  0  X  0  X  0  0  X  X  X  0  X  0  X  0  X  X  X  0  X  X  X  0  0  X  X  0  0  0
 0  0  0  0  0  X  0  X  X  0  0  0  X  X  0  X  X  0  0  X  0  X  0  0  X  X  0  X  X  X  0  X  0  X
 0  0  0  0  0  0  X  X  X  0  X  0  0  0  X  X  0  X  X  0  X  0  X  X  0  X  X  0  0  0  X  0  X  0

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+14x^29+38x^30+46x^32+70x^33+42x^37+21x^38+14x^40+2x^41+4x^46+3x^48+1x^54

The gray image is a linear code over GF(2) with n=68, k=8 and d=29.
This code was found by Heurico 1.16 in 2.44 seconds.