The generator matrix

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

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+54x^13+157x^14+382x^15+675x^16+1120x^17+1871x^18+2712x^19+3855x^20+5118x^21+6150x^22+6982x^23+7314x^24+7008x^25+6190x^26+5104x^27+3886x^28+2754x^29+1865x^30+1146x^31+634x^32+320x^33+147x^34+56x^35+19x^36+10x^37+4x^38+2x^39

The gray image is a linear code over GF(2) with n=48, k=16 and d=13.
This code was found by Heurico 1.11 in 43.8 seconds.