The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  1  0  X  X  0  1  0  0  1  0  1  1  1  0  0  1  X  1  0  X  0
 0  1  0  0  0  1  1  1 X+1  X  0  1  X  0  X  1  1  1  1 X+1  1  1  0  1  0  0 X+1  X  1  0  1  X  X  1  X
 0  0  1  0  1  1  0  1  1  X X+1  X  X  1 X+1  1 X+1  0  0  X  0 X+1  0  X X+1  X X+1  0  1  X X+1  X  0  1  X
 0  0  0  1  1  0  1 X+1  1 X+1  X  0  1  1 X+1  0  1  1  X X+1  0  0  1  1  1  X X+1  1 X+1  X X+1 X+1  1 X+1  0
 0  0  0  0  X  0  0  X  0  0  X  X  X  X  0  X  X  X  X  X  0  X  X  0  0  0  X  X  X  X  0  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  0  X  0  X  X  X  0  X  X  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  X  X  X  0  0  X  X  0  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+128x^28+284x^30+288x^32+375x^34+311x^36+251x^38+249x^40+101x^42+45x^44+13x^46+2x^48

The gray image is a linear code over GF(2) with n=70, k=11 and d=28.
This code was found by Heurico 1.16 in 0.27 seconds.