The generator matrix

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

generates a code of length 29 over Z4 who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+40x^19+124x^20+268x^21+383x^22+532x^23+703x^24+888x^25+1237x^26+1452x^27+1592x^28+1716x^29+1659x^30+1540x^31+1337x^32+1036x^33+730x^34+476x^35+308x^36+176x^37+77x^38+56x^39+31x^40+12x^41+9x^42+1x^46

The gray image is a code over GF(2) with n=58, k=14 and d=19.
This code was found by Heurico 1.10 in 3.97 seconds.