The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^19+254x^20+448x^21+742x^22+998x^23+1492x^24+1900x^25+2300x^26+2946x^27+3360x^28+3448x^29+3337x^30+3028x^31+2543x^32+2016x^33+1456x^34+970x^35+626x^36+360x^37+216x^38+118x^39+44x^40+20x^41+12x^42+6x^43+1x^46

The gray image is a code over GF(2) with n=58, k=15 and d=19.
This code was found by Heurico 1.16 in 45.5 seconds.