The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  1  0  1  1  1  X  1  0  X  0  1  1  1  1  1  1  0  X  1  1  1  X
 0  1  0  1  0  1  1  0  X  1 X+1  1  1  0  0  X  1  1  0 X+1  1  1  X  0  X  X  1  0 X+1  1  1  1 X+1  1  X
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  X  1 X+1  1  1  1  0  0  0  1  X X+1 X+1  X  1  0 X+1  1  0  X  0  X
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  0  X  X  X  0  X  X  0  0  0  X  X  X  X  0  0  0  X  X  0
 0  0  0  0  X  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  X  X  0  0  X  0  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  X  0  0  0  X  X  X  X  0  0  X  0  X  0  X  X  X  0  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  X  0  X  X  X  0  X  0  X  X  X  X  X  0  0  X  X  0  X  X  0  0  0  X
 0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  X  X  X  0  X  0

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+172x^28+178x^30+377x^32+288x^34+404x^36+236x^38+252x^40+64x^42+64x^44+2x^46+10x^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 0.283 seconds.