The generator matrix

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

generates a code of length 31 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+107x^20+114x^21+398x^22+474x^23+907x^24+982x^25+1470x^26+1938x^27+2396x^28+2872x^29+2863x^30+3444x^31+2949x^32+3132x^33+2412x^34+1940x^35+1583x^36+978x^37+804x^38+370x^39+351x^40+110x^41+110x^42+26x^43+26x^44+4x^45+7x^46

The gray image is a code over GF(2) with n=62, k=15 and d=20.
This code was found by Heurico 1.16 in 40.8 seconds.