The generator matrix

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

generates a code of length 29 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+242x^22+416x^24+618x^26+770x^28+776x^30+641x^32+428x^34+142x^36+46x^38+14x^40+2x^42

The gray image is a code over GF(2) with n=58, k=12 and d=22.
This code was found by Heurico 1.16 in 87.5 seconds.