The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+35x^24+84x^25+92x^26+104x^27+102x^28+88x^29+79x^30+74x^31+78x^32+76x^33+74x^34+52x^35+32x^36+24x^37+11x^38+10x^39+8x^40

The gray image is a code over GF(2) with n=60, k=10 and d=24.
This code was found by Heurico 1.10 in 0.015 seconds.