The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+69x^10+78x^11+150x^12+252x^13+443x^14+1706x^15+2762x^16+1736x^17+461x^18+258x^19+149x^20+60x^21+49x^22+6x^23+9x^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 0.14 seconds.