The generator matrix

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

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+73x^14+196x^15+344x^16+652x^17+957x^18+1310x^19+1899x^20+2532x^21+2992x^22+3476x^23+3768x^24+3468x^25+3155x^26+2632x^27+1842x^28+1356x^29+941x^30+552x^31+327x^32+184x^33+71x^34+26x^35+11x^36+2x^38+1x^42

The gray image is a linear code over GF(2) with n=48, k=15 and d=14.
This code was found by Heurico 1.16 in 21.8 seconds.