The generator matrix

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

generates a code of length 26 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+52x^16+106x^17+203x^18+346x^19+506x^20+772x^21+930x^22+1184x^23+1530x^24+1612x^25+1692x^26+1772x^27+1570x^28+1296x^29+986x^30+680x^31+505x^32+282x^33+153x^34+106x^35+60x^36+28x^37+4x^38+8x^39

The gray image is a code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.10 in 3.04 seconds.