The generator matrix

 1  1  1  1  1  1  1  1  1  2  1  2  2  0  1  2  2  1  1
 0  2  0  0  0  8  8  8  8  2 14  4 14  4 14  2 10 12  8
 0  0  2  0  0 12  6  2  2 10 14  4  0 12  4 14 12 10  0
 0  0  0  2  0  6  6  6  4 12  4  4  2  2 14 10  6  2  8
 0  0  0  0  2  2  4  6  2  4 14  2  8 14  8  8 12  2  4

generates a code of length 19 over Z16 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+110x^13+535x^14+1312x^15+2896x^16+6292x^17+12811x^18+17280x^19+13227x^20+6480x^21+2805x^22+1120x^23+451x^24+172x^25+41x^26+1x^28+2x^29

The gray image is a code over GF(2) with n=152, k=16 and d=52.
This code was found by Heurico 1.16 in 11.2 seconds.