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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+56x^28+8x^30+105x^32+80x^34+134x^36+40x^38+56x^40+25x^44+6x^48+1x^60

The gray image is a linear code over GF(2) with n=70, k=9 and d=28.
This code was found by Heurico 1.16 in 0.016 seconds.