The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+165x^20+272x^22+798x^24+1096x^26+1833x^28+1544x^30+1391x^32+600x^34+367x^36+72x^38+50x^40+3x^44

The gray image is a code over GF(2) with n=58, k=13 and d=20.
This code was found by Heurico 1.16 in 2.43 seconds.