The generator matrix

 1  1  1  1  2  1  1  2  2  1  1  1  1  1
 0 12  0 12 12  0 12 12 12  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  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  0  8
 0  0  0  0  0  0  0  8  0  0  8  0  8  8
 0  0  0  0  0  0  0  0  8  0  8  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+109x^8+224x^10+512x^11+392x^12+1536x^13+10752x^14+1536x^15+427x^16+512x^17+224x^18+88x^20+32x^22+7x^24

The gray image is a code over GF(2) with n=112, k=14 and d=24.
This code was found by Heurico 1.16 in 0.2 seconds.