The generator matrix

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

generates a code of length 31 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+277x^24+412x^26+648x^28+692x^30+773x^32+628x^34+416x^36+172x^38+61x^40+16x^42

The gray image is a code over GF(2) with n=62, k=12 and d=24.
This code was found by Heurico 1.10 in 17.3 seconds.