The generator matrix

 1  0  1  1  1  6  1  1 12  1 10  1  1  1  1  1
 0  1  3  6  5  1 12 15  1 10  1  3  9  5  3  5
 0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8
 0  0  0  8  0  0  0  8  0  8  0  8  0  8  8  0
 0  0  0  0  8  0  0  0  8  0  8  8  8  0  0  8
 0  0  0  0  0  8  0  8  8  0  0  8  0  0  8  8
 0  0  0  0  0  0  8  8  0  0  8  8  8  8  8  8

generates a code of length 16 over Z16 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+124x^12+128x^13+448x^14+2944x^15+909x^16+2944x^17+448x^18+128x^19+108x^20+10x^24

The gray image is a code over GF(2) with n=128, k=13 and d=48.
This code was found by Heurico 1.16 in 6.84 seconds.