The generator matrix

 1  0  0  1  1  1  6  1  1  1  2  1  0 12  1  8
 0  1  0  4  5 11  1 10  1 11  2  6  1  1  9  1
 0  0  1  7  3  4  3  3  1  2  1  0  6 10 15 15
 0  0  0  8  8  8  0  0  0  0  8  8  8  0  0  8

generates a code of length 16 over Z16 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+274x^13+980x^14+1394x^15+2931x^16+1404x^17+920x^18+236x^19+28x^20+18x^21+4x^22+2x^23

The gray image is a code over GF(2) with n=128, k=13 and d=52.
This code was found by Heurico 1.16 in 0.105 seconds.