The generator matrix

 1  1  1  1  1  1  1  2  0  1  0  1  1
 0  2  0  6  8  6 12 14  2  0  2 12  0
 0  0 12  0  8  4  4  8  4  4  8  0  4
 0  0  0 12 12  4  4 12 12 12  8 12  0

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

Homogenous weight enumerator: w(x)=1x^0+98x^10+112x^11+486x^12+672x^13+476x^14+112x^15+71x^16+18x^18+2x^20

The gray image is a code over GF(2) with n=104, k=11 and d=40.
This code was found by Heurico 1.16 in 5.09 seconds.