The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+58x^21+127x^22+218x^23+317x^24+392x^25+479x^26+580x^27+692x^28+764x^29+811x^30+800x^31+769x^32+656x^33+520x^34+396x^35+247x^36+170x^37+106x^38+54x^39+20x^40+8x^41+4x^42+1x^44+1x^48+1x^50

The gray image is a code over GF(2) with n=60, k=13 and d=21.
This code was found by Heurico 1.10 in 1.19 seconds.