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

generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+43x^24+16x^26+78x^28+48x^30+49x^32+17x^36+3x^40+1x^52

The gray image is a linear code over GF(2) with n=58, k=8 and d=24.
This code was found by Heurico 1.16 in 0.015 seconds.