The generator matrix

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

generates a code of length 29 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+81x^20+110x^21+238x^22+274x^23+425x^24+498x^25+607x^26+714x^27+686x^28+846x^29+696x^30+806x^31+649x^32+510x^33+418x^34+238x^35+193x^36+76x^37+82x^38+16x^39+13x^40+8x^41+7x^42

The gray image is a code over GF(2) with n=58, k=13 and d=20.
This code was found by Heurico 1.10 in 1.1 seconds.