The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+94x^20+76x^21+230x^22+334x^23+414x^24+522x^25+597x^26+646x^27+670x^28+850x^29+736x^30+794x^31+665x^32+534x^33+401x^34+258x^35+188x^36+58x^37+80x^38+16x^39+16x^40+8x^41+1x^42+2x^46+1x^50

The gray image is a code over GF(2) with n=58, k=13 and d=20.
This code was found by Heurico 1.16 in 2.67 seconds.