The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^16+104x^17+182x^18+294x^19+386x^20+500x^21+582x^22+688x^23+828x^24+832x^25+904x^26+828x^27+656x^28+520x^29+328x^30+224x^31+133x^32+88x^33+50x^34+14x^35+14x^36+4x^37+2x^38

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 1.94 seconds.