The generator matrix

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

generates a code of length 32 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+101x^20+520x^22+1205x^24+2344x^26+3888x^28+5188x^30+6105x^32+5384x^34+3989x^36+2280x^38+1189x^40+400x^42+150x^44+12x^46+12x^48

The gray image is a code over GF(2) with n=64, k=15 and d=20.
This code was found by Heurico 1.10 in 16.5 seconds.