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

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+23x^28+14x^30+16x^31+20x^32+48x^33+21x^34+48x^35+11x^36+16x^37+19x^38+7x^40+7x^42+2x^44+2x^46+1x^62

The gray image is a linear code over GF(2) with n=68, k=8 and d=28.
This code was found by Heurico 1.16 in -3.81e-008 seconds.