The generator matrix

 1  0  0  0  0  1  1  1  1  1  2  1  1  1  1  2  0  0  1  1  1  2  0  1  2  2  1  0  1
 0  1  0  0  0  0  0  0  1  3  1  2  0  3  3  1  1  2  1  2  0  1  1  1  1  1  1  0  1
 0  0  1  0  0  0  1  1  1  0  1  0  0  2  1  0  1  1  1  1  3  2  0  3  1  1  2  2  0
 0  0  0  1  0  1  1  0  0  1  1  2  3  2  1  1  2  3  1  3  2  3  2  2  0  2  1  1  2
 0  0  0  0  1  1  0  1  0  1  3  3  2  2  2  0  1  1  3  1  2  3  1  3  1  0  2  3  3
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  0  0  0  2  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  2
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  0  2  0  0  0  2  0  0  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+229x^20+740x^22+1645x^24+2194x^26+3226x^28+3388x^30+2673x^32+1416x^34+605x^36+192x^38+65x^40+6x^42+4x^44

The gray image is a code over GF(2) with n=58, k=14 and d=20.
This code was found by Heurico 1.16 in 89.2 seconds.