The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1
 0  8  0  0  0  0  0  0  0  0  0  8  0
 0  0  8  0  0  0  0  0  0  0  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  0
 0  0  0  0  0  0  0  0  8  0  0  8  0
 0  0  0  0  0  0  0  0  0  8  0  8  0
 0  0  0  0  0  0  0  0  0  0  8  8  0

generates a code of length 13 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+55x^4+11x^6+330x^8+165x^10+462x^12+14336x^13+462x^14+165x^16+330x^18+11x^20+55x^22+1x^26

The gray image is a code over GF(2) with n=104, k=14 and d=16.
This code was found by Heurico 1.16 in 0.108 seconds.