The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+40x^19+137x^20+286x^21+465x^22+730x^23+1072x^24+1448x^25+1822x^26+2360x^27+2935x^28+3226x^29+3410x^30+3328x^31+3023x^32+2516x^33+1948x^34+1524x^35+1035x^36+662x^37+389x^38+198x^39+112x^40+52x^41+30x^42+12x^43+5x^44+2x^45

The gray image is a code over GF(2) with n=60, k=15 and d=19.
This code was found by Heurico 1.10 in 14.7 seconds.