The generator matrix

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

generates a code of length 16 over Z16 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+70x^10+64x^11+161x^12+284x^13+410x^14+1688x^15+2795x^16+1736x^17+436x^18+256x^19+170x^20+60x^21+42x^22+8x^23+8x^24+2x^26+1x^28

The gray image is a code over GF(2) with n=128, k=13 and d=40.
This code was found by Heurico 1.16 in 0.176 seconds.