The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+49x^20+50x^21+154x^22+142x^23+263x^24+348x^25+437x^26+648x^27+704x^28+860x^29+852x^30+884x^31+729x^32+624x^33+479x^34+328x^35+249x^36+162x^37+114x^38+46x^39+47x^40+4x^41+11x^42+6x^44+1x^50

The gray image is a code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.16 in 2.59 seconds.