The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+91x^16+168x^17+310x^18+520x^19+694x^20+888x^21+1217x^22+1460x^23+1751x^24+2038x^25+1827x^26+1560x^27+1249x^28+946x^29+657x^30+468x^31+289x^32+114x^33+83x^34+24x^35+21x^36+6x^37+2x^38

The gray image is a code over GF(2) with n=50, k=14 and d=16.
This code was found by Heurico 1.10 in 3.04 seconds.