The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+147x^10+572x^12+208x^13+1345x^14+2816x^15+6056x^16+2976x^17+1463x^18+128x^19+519x^20+16x^21+115x^22+19x^24+2x^26+1x^28

The gray image is a code over GF(2) with n=128, k=14 and d=40.
This code was found by Heurico 1.16 in 13.5 seconds.