The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X  1  X  X  1  1  1  1  1  1  1  0  1
 0  1  0  0  0  1  1  1  0  0  1  1 X+1  1  X  0  X  X  X  X  0  X  0  X
 0  0  1  0  1  1  0  1  0  1  1  0  0 X+1  1  0  0  0  X  0  X  0  X  1
 0  0  0  1  1  0  1  1  1  0  1  1  X  0  1  0  1  1 X+1  1  1 X+1  1  X
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  0  X  0  0  X  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  0  X  0  X  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  X  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  0  X  X  0  X  0  X
 0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  0  X  X  0  X  X  0  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  0  X  0  X  0  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+12x^13+146x^14+96x^15+322x^16+392x^17+1136x^18+1192x^19+1184x^20+2636x^21+3674x^22+3904x^23+3800x^24+3824x^25+2576x^26+2576x^27+2432x^28+1252x^29+582x^30+416x^31+421x^32+72x^33+64x^34+8x^35+32x^36+4x^37+14x^38

The gray image is a linear code over GF(2) with n=48, k=15 and d=13.
This code was found by Heurico 1.16 in 13.6 seconds.