The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+228x^20+318x^22+1232x^24+1670x^26+3095x^28+3180x^30+3237x^32+1708x^34+1231x^36+278x^38+168x^40+14x^42+21x^44+2x^48+1x^52

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 35.7 seconds.