The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  2  2  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  2  2  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  0  0  2  0  2  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  0  2  0  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  0  0  2  2  2  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  2  0  2  2  2  0  0  0  2  2  2
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  0  0  2  2  0  0  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  0  0  2  0  2  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  2  2  2  0  0  0  2  2  0  0  2  2
 0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  0  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+52x^20+56x^22+104x^24+102x^26+128x^27+120x^28+384x^29+123x^30+384x^31+147x^32+128x^33+148x^34+68x^36+59x^38+20x^40+22x^42+1x^46+1x^54

The gray image is a code over GF(2) with n=60, k=11 and d=20.
This code was found by Heurico 1.16 in 0.342 seconds.