The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+41x^20+88x^22+32x^23+173x^24+104x^25+256x^26+328x^27+429x^28+640x^29+658x^30+928x^31+742x^32+976x^33+714x^34+624x^35+475x^36+320x^37+268x^38+128x^39+135x^40+8x^41+52x^42+8x^43+47x^44+10x^46+5x^48+2x^50

The gray image is a code over GF(2) with n=64, k=13 and d=20.
This code was found by Heurico 1.16 in 2.86 seconds.