The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  0  1  1  1  1  0  2  0  0  1  1  1  2  2  2  0  1  2  1
 0  1  0  1  0  1  1  0  0  1  1  1  1  2  0  0  1  3  1  1  0  1  3  3  0  1  1  1  1  1  1  0
 0  0  1  1  1  0  1  0  1  1  0  2  1  1  0  3  3  0  0  1  1  0  0  2  2  1  1  1  0  1  1  0
 0  0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  2  2  0  0  2  0  2  0  0  0  2  0  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  0  2  2  2  2  0  0  2  0  0  0  0  2  2  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  0  0  2  0  2  2  0  0  2  2  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  0  2  2  0  0  0  2  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  0  2  2  2  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  0  0  2  2  2  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  2  2  2  0  0  2  0  2  0  2  2  2  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  2  2  2  0  2  0  0  2  2  0  2  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+42x^20+24x^21+147x^22+114x^23+255x^24+386x^25+544x^26+738x^27+937x^28+1178x^29+1343x^30+1620x^31+1604x^32+1652x^33+1388x^34+1284x^35+977x^36+716x^37+545x^38+314x^39+245x^40+138x^41+112x^42+26x^43+27x^44+2x^45+13x^46+7x^48+4x^50+1x^52

The gray image is a code over GF(2) with n=64, k=14 and d=20.
This code was found by Heurico 1.16 in 9.86 seconds.