The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+113x^20+302x^22+677x^24+902x^26+1399x^28+1332x^30+1482x^32+996x^34+575x^36+286x^38+95x^40+22x^42+9x^44+1x^48

The gray image is a code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.10 in 1.11 seconds.