The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  0  1  1  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0 X+1  1  0  1 X+1  0  0 X+1 X+1  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  0  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  X  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  0  0  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  0  0  X  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  X  X  X  0  0  0  0

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+56x^12+272x^14+263x^16+848x^18+1736x^20+2976x^22+4080x^24+2976x^26+1736x^28+848x^30+263x^32+272x^34+56x^36+1x^48

The gray image is a linear code over GF(2) with n=48, k=14 and d=12.
This code was found by Heurico 1.16 in 3.1 seconds.