The generator matrix

 1  1  1  1  1  1  1  1  2  0  2 12  1  1
 0  2 12  6  8 14  4 10  6  2 10  2  0 12

generates a code of length 14 over Z16 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+40x^13+44x^14+40x^15+1x^16+2x^20

The gray image is a code over GF(2) with n=112, k=7 and d=52.
This code was found by Heurico 1.16 in 0.000973 seconds.