The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  X  0  1  1  0  0  0  1  1  X  X  1  1  1  1  X  X  1  X  1
 0  1  0  0  0  1  1  1  0  0  1 X+1  1  0  1  1  X  0  0  1  1  X  X  1  1  0  X X+1 X+1 X+1  0  X  X  1  1
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  X  1 X+1  0  X  1  0 X+1  0 X+1  1  X  1  0  0  1  1  0  0  1
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  0  X  X  1  1  1 X+1  1  X  1  X  1  0  0  0 X+1  X X+1 X+1  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  X  0  0  X  0  X  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  X  0  0  0  X  X  0  X  0  X  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  X  X  X  0  X  0  0  X  0  X  X  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  0  X  0  0  X  0  X  0  X  0  X  0  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  0  X  0  0  X  X  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  0  X  0  X  X  X  X  X  X  0  X  0  X  X  0  0  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  0  0  X  X  0  0  0  X  X  0  0  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+283x^24+602x^26+1770x^28+2744x^30+4871x^32+5870x^34+6406x^36+4640x^38+3324x^40+1366x^42+678x^44+136x^46+64x^48+2x^50+10x^52+1x^56

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 72 seconds.