The generator matrix

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

generates a code of length 14 over Z16 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+37x^6+52x^7+149x^8+268x^9+437x^10+1188x^11+1392x^12+2588x^13+20546x^14+2588x^15+1379x^16+1188x^17+458x^18+268x^19+144x^20+52x^21+25x^22+7x^24+1x^26

The gray image is a code over GF(2) with n=112, k=15 and d=24.
This code was found by Heurico 1.16 in 0.541 seconds.