The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^14+180x^15+317x^16+522x^17+849x^18+1356x^19+1853x^20+2442x^21+3180x^22+3648x^23+3811x^24+3540x^25+3210x^26+2784x^27+1938x^28+1300x^29+854x^30+460x^31+262x^32+130x^33+45x^34+20x^35+9x^36+2x^37+1x^40

The gray image is a code over GF(2) with n=48, k=15 and d=14.
This code was found by Heurico 1.10 in 9.13 seconds.