The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^20+94x^21+221x^22+286x^23+402x^24+472x^25+552x^26+728x^27+777x^28+900x^29+812x^30+772x^31+631x^32+504x^33+392x^34+248x^35+156x^36+78x^37+61x^38+14x^39+14x^40+8x^42+1x^44+2x^46

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 2.64 seconds.