The generator matrix

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

generates a code of length 19 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+100x^14+64x^15+414x^16+672x^17+1806x^18+2112x^19+1791x^20+672x^21+376x^22+64x^23+97x^24+22x^26+1x^28

The gray image is a code over GF(2) with n=152, k=13 and d=56.
This code was found by Heurico 1.16 in 0.34 seconds.