The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+208x^24+306x^28+128x^30+1005x^32+768x^34+1033x^36+128x^38+360x^40+129x^44+26x^48+3x^52+1x^60

The gray image is a linear code over GF(2) with n=68, k=12 and d=24.
This code was found by Heurico 1.16 in 6.23 seconds.