The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^20+402x^22+947x^24+1474x^26+2310x^28+2872x^30+3032x^32+2360x^34+1572x^36+846x^38+337x^40+102x^42+22x^44+8x^46+3x^48

The gray image is a code over GF(2) with n=62, k=14 and d=20.
This code was found by Heurico 1.10 in 4.26 seconds.