The generator matrix

 1  0  1  1  1  6  1  1  0  1  1  1  1  1
 0  1  3  6  5  1 12  3  1  0  0  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  8  0  8
 0  0  0  8  0  0  0  0  0  0  0  8  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  8  8
 0  0  0  0  0  8  0  0  0  0  8  0  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  8  0
 0  0  0  0  0  0  0  8  0  0  8  8  0  8
 0  0  0  0  0  0  0  0  8  0  0  8  8  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+32x^6+16x^7+173x^8+112x^9+608x^10+592x^11+4424x^12+12592x^13+28416x^14+12592x^15+4459x^16+592x^17+608x^18+112x^19+152x^20+16x^21+32x^22+7x^24

The gray image is a code over GF(2) with n=112, k=16 and d=24.
This code was found by Heurico 1.16 in 0.999 seconds.