The generator matrix

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

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+52x^14+14x^15+162x^16+56x^17+256x^18+346x^19+296x^20+528x^21+708x^22+1116x^23+1112x^24+1088x^25+736x^26+516x^27+336x^28+368x^29+252x^30+54x^31+133x^32+8x^33+32x^34+2x^35+8x^36+12x^38

The gray image is a linear code over GF(2) with n=48, k=13 and d=14.
This code was found by Heurico 1.16 in 1.36 seconds.