The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  1  1  1  1  2  0  0  1  1  2  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  3  1  3  2  1  1  2  3  1  1  2
 0  0  1  0  0  0  1  1  1  1  1  0  0  3  0  3  2  3  1  3  1  0  3  0
 0  0  0  1  0  1  1  0  1  0  1  1  1  1  0  2  1  3  0  3  0  3  0  0
 0  0  0  0  1  1  0  1  1  0  1  1  0  2  1  1  3  0  1  2  0  0  2  1
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2
 0  0  0  0  0  0  2  0  0  0  0  2  0  2  0  0  2  2  2  2  0  0  0  2
 0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2
 0  0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  0  0  2  2  2  2  0  2

generates a code of length 24 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+57x^14+138x^15+326x^16+530x^17+894x^18+1164x^19+1908x^20+2760x^21+3163x^22+3468x^23+3672x^24+3900x^25+3132x^26+2480x^27+2016x^28+1384x^29+871x^30+410x^31+257x^32+130x^33+70x^34+20x^35+12x^36+5x^38

The gray image is a code over GF(2) with n=48, k=15 and d=14.
This code was found by Heurico 1.16 in 17.6 seconds.