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 12 15 15
 0  0  1  7  1  4  3  2  4  2  5  3  6
 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+150x^10+860x^11+1593x^12+3036x^13+1548x^14+820x^15+157x^16+20x^17+6x^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 0.094 seconds.