The generator matrix

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

generates a code of length 16 over Z16 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+85x^8+76x^10+64x^11+296x^12+576x^13+320x^14+4480x^15+4539x^16+4480x^17+440x^18+576x^19+184x^20+64x^21+160x^22+15x^24+28x^26

The gray image is a code over GF(2) with n=128, k=14 and d=32.
This code was found by Heurico 1.16 in 0.224 seconds.