The generator matrix

 1  0  1  1  1 12  1  1  1  1  2  1  1  2  1  1
 0  1  1  0 11  1  6  7 10  3  1  6  9 14 10  2
 0  0  2  6  0  2  0  2  2  4  6  8 10  6  6  2
 0  0  0 12  0  0  4 12  8  4 12  8  4  8  8 12
 0  0  0  0 12 12  4  4 12  8  8  8  8 12  0 12

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

Homogenous weight enumerator: w(x)=1x^0+74x^11+350x^12+914x^13+3008x^14+6888x^15+10179x^16+7092x^17+3024x^18+810x^19+314x^20+90x^21+16x^22+4x^23+4x^24

The gray image is a code over GF(2) with n=128, k=15 and d=44.
This code was found by Heurico 1.16 in 1.63 seconds.