The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  0  0  1  1  1  0  1  1  X  0  1  0  0  X  1  1  X  X  0  0  1  0
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  X X+1  0  X  1  0  1  1  1 X+1  1  0  X  X X+1  X  0  1  1  X  X
 0  0  1  0  0  0  1  1  1  1 X+1  0  0 X+1  X  X  X  0  1 X+1  X  0  0 X+1 X+1  1  0  1  X  1  1  X  1  1  1
 0  0  0  1  0  1  1  0  1  X X+1  1  0  1  1  1  X  1 X+1  1  0  X  1 X+1  X  1  0  0 X+1  X  X X+1  X  X  1
 0  0  0  0  1  1  0  1 X+1  X X+1 X+1  1  X X+1  0  1  0 X+1  1  0  1  X  X  0  X  1 X+1 X+1  X  1 X+1 X+1  0  0
 0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  X  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  X  X  0  X  X  0  X  0  X  0  X  X  0  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  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+159x^26+509x^28+817x^30+1176x^32+1417x^34+1428x^36+1248x^38+837x^40+423x^42+127x^44+31x^46+17x^48+1x^50+1x^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 3.9 seconds.