The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  X  1  1  X  1  X  X  1  1  1  0  1  1  1
 0  1  1  0  1  1  0 X+1  1 X+1  0  1  0 X+1  1  0 X+1  1  X X+1  1  X  1  X  0  1  X  0  0  X  X  0  X  0
 0  0  X  0  0  0  0  0  X  X  0  X  X  X  0  X  X  0  X  0  X  X  0  0  X  X  0  X  X  X  0  0  0  0
 0  0  0  X  0  0  X  0  X  X  X  0  X  X  0  0  0  X  0  0  0  X  0  X  X  0  0  X  0  X  X  0  X  X
 0  0  0  0  X  0  X  X  0  0  X  0  0  X  X  0  X  X  0  X  0  0  X  X  X  0  X  0  0  X  0  X  X  0
 0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  0  X  X  0  X  0  X  X  X  0  0  X  0  0  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+29x^30+52x^31+43x^32+16x^34+56x^35+6x^36+14x^38+20x^39+10x^40+2x^44+5x^46+2x^48

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 0.419 seconds.