The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+20x^19+55x^20+124x^21+221x^22+308x^23+378x^24+494x^25+600x^26+694x^27+790x^28+798x^29+782x^30+710x^31+628x^32+530x^33+396x^34+286x^35+179x^36+94x^37+45x^38+30x^39+16x^40+8x^41+4x^42+1x^48

The gray image is a code over GF(2) with n=58, k=13 and d=19.
This code was found by Heurico 1.10 in 1.03 seconds.