The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  1  X  X  X  X  1  1  X  1  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  X  X  0  0  0  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  0  0  X  0  X  X  0  X  X  0  0  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  0  X  X  0  X  X  X  0  X  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0  0  X  X  0  0  X  X  0  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  0  X  X  X  0  0  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  0  X  0  X  X  0  X  X  0  X  0  0  X
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  0  X  0  0  X  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  0  X  0  0  0  X  X  X  0  X  0  0  X  X  0  X
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  0  X  X  X  X  X  0  0  X  0  X  X  0  0  X  0  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  0  0  0  0  0  X  X  0  0  X  X  0  X  0  X

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+145x^24+8x^26+375x^28+176x^30+750x^32+448x^34+950x^36+336x^38+595x^40+56x^42+200x^44+45x^48+10x^52+1x^60

The gray image is a linear code over GF(2) with n=70, k=12 and d=24.
This code was found by Heurico 1.16 in 1.41 seconds.