The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  0  1  1  1  1  2  0  0  2  1  1  0  2  1  1  2  2  0  2
 0  1  0  1  0  1  1  0  0  1  1  1  1  0  2  1  2  3  1  1  0  1  0  1  1  1  3  3  1  1  2  0
 0  0  1  1  1  0  1  0  1  1  0  0  1  1  2  1  3  0  3  0  1  1  2  1  0  2  0  0  3  1  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  2  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  0  0  2  0  2  0  2  0  0  2  2  0  2  0  2  2  2
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  2  2  0  0  0  2  2  0  2  0  0  0  2  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  0  0  0  0  0  2  0  2  2  0  0  2
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  0  0  0  2  0  0  2  0  2  0  2  2  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  2  0  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  0  0  2  2  0  2
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  2  2  0  2  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  2  2  2  0  0  0  0  0  2  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+180x^20+214x^22+1198x^24+1816x^26+4305x^28+5062x^30+7009x^32+5312x^34+4423x^36+1698x^38+1150x^40+232x^42+143x^44+2x^46+18x^48+5x^52

The gray image is a code over GF(2) with n=64, k=15 and d=20.
This code was found by Heurico 1.16 in 35.4 seconds.