The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+322x^20+596x^22+1540x^24+2368x^26+3324x^28+3240x^30+2763x^32+1312x^34+666x^36+164x^38+80x^40+8x^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 44.1 seconds.