The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+16x^13+28x^14+16x^15+1x^16+2x^20

The gray image is a code over GF(2) with n=112, k=6 and d=52.
This code was found by Heurico 1.16 in 0.000734 seconds.