The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+147x^26+536x^28+829x^30+1150x^32+1341x^34+1530x^36+1228x^38+854x^40+383x^42+142x^44+39x^46+9x^48+1x^50+2x^56

The gray image is a linear code over GF(2) with n=70, k=13 and d=26.
This code was found by Heurico 1.16 in 3.98 seconds.