The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  0  1  1  1  0  1  1  0  1  1  2  2  0  1  0  1
 0  1  1  0  1  1  0  1  1  0  3  1  0  1  3  0  3  1  3  2  1  3  0  0  1  1  3  1  3
 0  0  2  0  0  0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  2  0  0  2  2  2  2
 0  0  0  2  0  0  0  0  0  0  0  0  2  2  0  0  0  2  0  2  0  2  2  0  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  2  2  0  2  0  2  0  2  2  2  2  2  0  2  2  0  0  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  0  2  0  2  2  2  0  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  2  0  2  0  2  2  0  2  2
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  0  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  2  2  2  2  0  0  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+119x^20+102x^22+478x^24+480x^26+934x^28+668x^30+733x^32+272x^34+259x^36+14x^38+35x^40+1x^56

The gray image is a code over GF(2) with n=58, k=12 and d=20.
This code was found by Heurico 1.16 in 0.785 seconds.