The generator matrix

 1  0  1  1  1  4  1  0  1  1  1  6  1  0  1 12
 0  1  1  0  3  1  0  1  9  0  5  1 14  1  8  4
 0  0  2  0  2  4 14 10  0 14  4 14 14  6 10  2
 0  0  0  2  2  6 14  2  2 12  0  8 12  4 12  8
 0  0  0  0  4  0  8  0 12  4  4  0  8 12  4 12

generates a code of length 16 over Z16 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+190x^11+644x^12+1826x^13+5755x^14+15050x^15+18408x^16+15292x^17+5862x^18+1786x^19+498x^20+146x^21+63x^22+14x^23+1x^24

The gray image is a code over GF(2) with n=128, k=16 and d=44.
This code was found by Heurico 1.16 in 17.5 seconds.