The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^20+104x^22+48x^23+252x^24+192x^25+310x^26+448x^27+563x^28+832x^29+719x^30+1056x^31+752x^32+832x^33+619x^34+448x^35+336x^36+192x^37+238x^38+48x^39+66x^40+44x^42+11x^44+11x^46+1x^48+3x^50

The gray image is a code over GF(2) with n=62, k=13 and d=20.
This code was found by Heurico 1.16 in 2.89 seconds.