The generator matrix

 1  0  0  1  1  1  6  1  1  1  1  1  1
 0  1  0  4  1 11  1  4 14  2 15  1  6
 0  0  1  7  1  4  3  2  4  2  6  7  5
 0  0  0  8  8  8  0  0  0  8  0  0  8

generates a code of length 13 over Z16 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+186x^10+724x^11+1817x^12+2788x^13+1764x^14+700x^15+189x^16+12x^17+10x^18+1x^20

The gray image is a code over GF(2) with n=104, k=13 and d=40.
This code was found by Heurico 1.16 in 0.0984 seconds.