The generator matrix

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

generates a code of length 25 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+119x^16+206x^18+746x^20+1104x^22+2009x^24+1692x^26+1356x^28+544x^30+348x^32+38x^34+26x^36+3x^40

The gray image is a code over GF(2) with n=50, k=13 and d=16.
This code was found by Heurico 1.16 in 1.77 seconds.