The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  2  2  2  1  1  2  2  1  1  1  1  2  1  2  2  1  0  2
 0  1  0  0  0  1  1  1  0  0  3  3  1  0  1  2  3  2  1  2  1  0  2  1  1  1  0  2  2  1
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  1  2  0  3  1  3  0  2  1  0  3  1  1  1  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  0  2  0  1  2  3  2  0  1  1  3  3  0  0  0  1
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  2  0  0  0  2  2  2  2  2  0  0  0  2  2
 0  0  0  0  0  0  2  0  0  0  2  2  0  2  2  2  2  2  0  0  2  0  0  2  0  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  0  2  0  2  0  2  0  0  2  2  2  2  2  2  0  2  0  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  0  0  2  0  2  2  0  2  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  0  2  2  0  2  2  0  2  2  2  0  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+75x^20+110x^21+300x^22+302x^23+553x^24+788x^25+903x^26+1202x^27+1426x^28+1598x^29+1645x^30+1780x^31+1423x^32+1312x^33+1014x^34+716x^35+527x^36+274x^37+214x^38+94x^39+85x^40+12x^41+19x^42+2x^43+4x^44+2x^45+1x^46+2x^48

The gray image is a code over GF(2) with n=60, k=14 and d=20.
This code was found by Heurico 1.16 in 18.3 seconds.