The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  X  X  1  X  X  0  0  1  0  1  1  1  1  1  1  0  1  X  X  1  1  0
 0  1  0  0  0  0  0  0  0  1 X+1  1  1  1  0 X+1  1  X  1  1  X  1 X+1  X  1  1 X+1  X  1  X  1  1  X  X  X
 0  0  1  0  0  0  1  1  1  1  1  0  0  X  1  1  1  0  1  X  0 X+1  0  1  0  0  1  X X+1  1  1  0  X  X  X
 0  0  0  1  0  1  1  0  1  0  0  1 X+1  X  1 X+1  X  1 X+1 X+1  X  0  0  1  X X+1 X+1  0 X+1  0 X+1  0 X+1 X+1  X
 0  0  0  0  1  1  0  1  1  0  1  0  X  1  X  0  0  1  0 X+1  1 X+1  X  1 X+1  1  1  0  0  0 X+1 X+1  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  0  0  X  X  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  0  X  X  X  0  0  0  X  0  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  X  0  X  X  X  X  0  0  0  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  X  0  X  X  X  X  0  X  X  X  X  0  0  0  0  X  0  X  X  0  0  0  X  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+236x^24+690x^26+1846x^28+2900x^30+4647x^32+5804x^34+6314x^36+4776x^38+3072x^40+1514x^42+714x^44+180x^46+60x^48+8x^50+6x^52

The gray image is a linear code over GF(2) with n=70, k=15 and d=24.
This code was found by Heurico 1.16 in 47.6 seconds.