The generator matrix

 1  1  1  1  1  1  1  1  2  2  2  1  1  2  1  1
 0 12  0  4  0  0  4 12  8  4 12  8  0  0 12 12
 0  0 12  4  0 12  4  0  4  4  0 12  0 12  8  0
 0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  8
 0  0  0  0  8  0  0  0  8  8  0  8  8  8  0  0
 0  0  0  0  0  8  0  0  8  0  0  8  0  8  0  8
 0  0  0  0  0  0  8  0  8  8  8  8  8  0  0  8
 0  0  0  0  0  0  0  8  8  0  8  0  8  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+78x^10+206x^12+128x^13+574x^14+384x^15+5455x^16+384x^17+570x^18+128x^19+210x^20+58x^22+16x^24

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 16.9 seconds.