The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1  1  0  1  1  2  0  0  2  0  0  1  1  1
 0  1  0  0  0  0  0  0  0  3  1  3  3  1  2  1  2  1  1  0  1  1  0  3  2
 0  0  1  0  0  0  1  1  1  1  1  2  0  1  3  0  1  2  1  1  3  0  3  1  0
 0  0  0  1  0  1  1  0  1  0  0  2  1  1  1  0  1  3  3  0  0  1  2  1  0
 0  0  0  0  1  1  0  1  1  1  0  0  3  1  3  1  2  3  0  3  3  0  2  2  1
 0  0  0  0  0  2  0  0  0  0  2  2  0  2  2  0  0  2  0  2  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  2  2  0  0  2  0  0  0  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  2  0  2  0  2  2  2  0
 0  0  0  0  0  0  0  0  2  2  0  2  0  0  2  2  2  0  2  2  0  2  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+110x^16+156x^17+294x^18+488x^19+690x^20+944x^21+1204x^22+1564x^23+1756x^24+1876x^25+1800x^26+1580x^27+1280x^28+988x^29+708x^30+436x^31+245x^32+128x^33+82x^34+28x^35+14x^36+4x^37+8x^38

The gray image is a code over GF(2) with n=50, k=14 and d=16.
This code was found by Heurico 1.16 in 13.1 seconds.