The generator matrix

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

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+34x^16+80x^17+130x^18+192x^19+235x^20+312x^21+408x^22+432x^23+432x^24+424x^25+396x^26+352x^27+275x^28+200x^29+88x^30+48x^31+45x^32+8x^33+2x^34+1x^36+1x^44

The gray image is a linear code over GF(2) with n=48, k=12 and d=16.
This code was found by Heurico 1.16 in 0.451 seconds.