The generator matrix

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

generates a code of length 31 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+302x^22+816x^24+1498x^26+2406x^28+3042x^30+3262x^32+2574x^34+1466x^36+724x^38+224x^40+48x^42+16x^44+4x^46+1x^48

The gray image is a code over GF(2) with n=62, k=14 and d=22.
This code was found by Heurico 1.10 in 11.6 seconds.