The generator matrix

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

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+355x^16+888x^18+1983x^20+2960x^22+3834x^24+3248x^26+1990x^28+784x^30+274x^32+56x^34+11x^36

The gray image is a linear code over GF(2) with n=48, k=14 and d=16.
This code was found by Heurico 1.16 in 16.6 seconds.