The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+248x^22+415x^24+592x^26+796x^28+752x^30+702x^32+370x^34+155x^36+52x^38+10x^40+2x^42+1x^44

The gray image is a code over GF(2) with n=58, k=12 and d=22.
This code was found by Heurico 1.09 in 25.8 seconds.