The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1  1  1  0  0  2  1  1  0  1  1  1  1  1  2  1  0  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  3  1  1  2  3  0  1  2  2  0  1  3  2  2  1  3  3  0  0
 0  0  1  0  0  0  1  1  1  1  1  0  0  0  3  2  1  3  3  1  2  0  1  2  3  0  0  2  1  1  0  0
 0  0  0  1  0  1  1  0  1  0  1  1  0  2  0  3  0  3  3  1  3  0  0  3  1  1  3  2  3  1  0  0
 0  0  0  0  1  1  0  1  1  0  1  0  1  2  3  1  3  2  3  3  0  3  0  3  3  1  2  1  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  0  0  0  0  0  2  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  2  2  0  2  2  2  0  0  2  0  0  2  0  0  2  0  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  0  2  0  2  2  0  2  2  0  2  2  2  2  0  0  2  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  2  2  0  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+37x^20+54x^21+253x^22+306x^23+561x^24+724x^25+1154x^26+1416x^27+1993x^28+2470x^29+2672x^30+3166x^31+3004x^32+3208x^33+2700x^34+2592x^35+2023x^36+1458x^37+1202x^38+654x^39+511x^40+260x^41+194x^42+56x^43+59x^44+18x^45+16x^46+2x^47+3x^48+1x^54

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 37.4 seconds.