The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+130x^24+60x^26+530x^28+496x^30+1392x^32+1352x^34+1847x^36+944x^38+925x^40+220x^42+245x^44+47x^48+1x^52+1x^56+1x^60

The gray image is a linear code over GF(2) with n=70, k=13 and d=24.
This code was found by Heurico 1.16 in 3.99 seconds.