The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  1  0  X  0  1  1  1  1  1  1  0  X  0  1  1  1  1  1  X  0  X  X  X  0
 0  1  0  1  0  1  1  0  0  1 X+1  X  1  1  0  0  X  X  1  1 X+1  0  1  0  X X+1  X X+1  1  0  1  1  1  0  0
 0  0  1  1  1  0  1  0  1 X+1  X  1  X  1  1  0  0  1  1  1  0  1  1  1  1  0 X+1  0  1  1 X+1  X  X  1  1
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  X  X  0  X  0  0  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  0  X  0  X  0  X  X  X  0  X  0  X  0  0  X  0  0  X
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  0  0  X  X  X  X  X  0  0  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  X  X  0  X  X  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  X  X  0  X  0  X  0  X  0  0  0  0  X  0  X  0  X  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  X  X  0  X  0  X  X  0  0  0  0  0  0  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+73x^26+226x^28+443x^30+602x^32+686x^34+745x^36+630x^38+402x^40+181x^42+68x^44+31x^46+3x^48+4x^50+1x^52

The gray image is a linear code over GF(2) with n=70, k=12 and d=26.
This code was found by Heurico 1.16 in 1.02 seconds.