The generator matrix

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

generates a code of length 14 over Z16 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+4x^12+28x^13+68x^14+16x^15+3x^16+4x^17+4x^18

The gray image is a code over GF(2) with n=112, k=7 and d=48.
This code was found by Heurico 1.16 in 0.00102 seconds.