The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+37x^14+50x^15+159x^16+234x^17+490x^18+640x^19+944x^20+1304x^21+1521x^22+1868x^23+1871x^24+1852x^25+1532x^26+1320x^27+984x^28+664x^29+471x^30+210x^31+128x^32+42x^33+42x^34+8x^35+8x^36+3x^38+1x^40

The gray image is a code over GF(2) with n=48, k=14 and d=14.
This code was found by Heurico 1.16 in 9.15 seconds.