The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^21+103x^22+262x^23+338x^24+378x^25+509x^26+526x^27+671x^28+776x^29+825x^30+856x^31+753x^32+656x^33+493x^34+368x^35+259x^36+174x^37+116x^38+34x^39+23x^40+22x^41+2x^42+2x^43+2x^44+1x^48

The gray image is a code over GF(2) with n=60, k=13 and d=21.
This code was found by Heurico 1.16 in 2.93 seconds.