The generator matrix

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

generates a code of length 31 over Z4 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+16x^21+73x^22+176x^23+229x^24+288x^25+404x^26+452x^27+623x^28+682x^29+719x^30+774x^31+723x^32+802x^33+638x^34+502x^35+404x^36+238x^37+189x^38+130x^39+63x^40+22x^41+22x^42+14x^43+5x^44+3x^46

The gray image is a code over GF(2) with n=62, k=13 and d=21.
This code was found by Heurico 1.10 in 1.2 seconds.