The generator matrix

 1  1  1  1  1  1  1  1  2  1  4  1  2
 0 12  0  0  8 12 12  4  0 12  4  8  0
 0  0 12  0 12 12  4  0  8 12  8  8  4
 0  0  0 12  4  8 12 12  4 12 12  0 12

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

Homogenous weight enumerator: w(x)=1x^0+62x^10+24x^11+273x^12+336x^13+236x^14+24x^15+53x^16+14x^18+1x^20

The gray image is a code over GF(2) with n=104, k=10 and d=40.
This code was found by Heurico 1.16 in 0.171 seconds.