The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+94x^20+98x^21+310x^22+390x^23+660x^24+760x^25+931x^26+1154x^27+1293x^28+1586x^29+1536x^30+1766x^31+1359x^32+1310x^33+1058x^34+702x^35+596x^36+324x^37+226x^38+76x^39+84x^40+18x^41+35x^42+8x^43+9x^44

The gray image is a code over GF(2) with n=60, k=14 and d=20.
This code was found by Heurico 1.10 in 4.26 seconds.