The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  0  1  0  1  X  0  1  0  1  1  1  1  1  0  1  0  0  1  0
 0  1  0  1  0  1  1  0  0  1  1  1  1  X  X  X  0  1  1 X+1  1  0  X  1 X+1  X X+1 X+1  X  X  X  1  1 X+1  1
 0  0  1  1  1  0  1  0  1  1  0  X  1  1  1  0  1  1  0  0 X+1  1  1  0  0  X  0  1 X+1  1  0 X+1  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  X  0  X  0  X  0  0  X  0  0  0  0  X  0  X  0  X  X  0  X  0  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  0  X  X  0  0  X  0  0  X  X  0  0  0  X  0  0  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0  X  X  X  0  0  X  X  X  0  0  0  0  X  X  0  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  X  X  0  X  X  X  0  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  X  X  X  0  X  0  X  X  X  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  0  0  X  X  0  X  X  X  0  X  0  X  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  X  0  X  0  X  X  X  0  X  X  X  0  0  0  X  0  0  X  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  0  X  X  X  X  0  0  X  0  0  X  0  X  0  0  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+194x^24+288x^26+965x^28+1240x^30+2586x^32+2736x^34+3233x^36+2272x^38+1761x^40+560x^42+399x^44+72x^46+65x^48+11x^52+1x^56

The gray image is a linear code over GF(2) with n=70, k=14 and d=24.
This code was found by Heurico 1.16 in 13.7 seconds.