The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+239x^20+970x^22+2162x^24+3670x^26+5838x^28+6786x^30+6031x^32+3984x^34+1987x^36+786x^38+246x^40+58x^42+8x^44+2x^46

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 98.8 seconds.