The generator matrix

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

generates a code of length 31 over Z4 who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+54x^19+137x^20+224x^21+384x^22+594x^23+820x^24+1216x^25+1568x^26+1894x^27+2237x^28+2598x^29+3116x^30+3030x^31+2867x^32+2792x^33+2392x^34+2058x^35+1523x^36+1140x^37+848x^38+502x^39+328x^40+200x^41+136x^42+58x^43+23x^44+22x^45+4x^46+2x^47

The gray image is a code over GF(2) with n=62, k=15 and d=19.
This code was found by Heurico 1.10 in 14.7 seconds.