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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+28x^30+54x^32+48x^34+48x^36+48x^38+24x^40+4x^46+1x^64

The gray image is a linear code over GF(2) with n=70, k=8 and d=30.
This code was found by Heurico 1.16 in 0.0228 seconds.