The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^20+122x^21+243x^22+376x^23+567x^24+750x^25+1004x^26+1188x^27+1351x^28+1632x^29+1595x^30+1660x^31+1473x^32+1256x^33+984x^34+772x^35+550x^36+310x^37+241x^38+92x^39+55x^40+26x^41+28x^42+8x^43+3x^44+1x^46

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 19.4 seconds.