The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+370x^20+762x^22+2108x^24+3674x^26+6217x^28+6452x^30+6205x^32+3780x^34+2193x^36+658x^38+292x^40+34x^42+19x^44+2x^48+1x^52

The gray image is a code over GF(2) with n=60, k=15 and d=20.
This code was found by Heurico 1.16 in 99.4 seconds.