The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  8  1  1  2  1
 0  1 11  6  5  1  0 11  1 14  1  1  7  8 14 11
 0  0 12  0  0  4  4  8  4 12 12  0  8  0  4 12
 0  0  0 12  0  4  4  4  0  8  8 12  4 12  8  8
 0  0  0  0  8  0  8  8  0  0  8  0  8  8  8  8
 0  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+62x^11+137x^12+426x^13+1481x^14+3600x^15+4964x^16+3620x^17+1479x^18+430x^19+111x^20+50x^21+15x^22+4x^23+3x^24+1x^26

The gray image is a code over GF(2) with n=128, k=14 and d=44.
This code was found by Heurico 1.16 in 1.88 seconds.