The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^14+406x^15+740x^16+1490x^17+3419x^18+3862x^19+3654x^20+1588x^21+650x^22+290x^23+117x^24+42x^25+7x^26+2x^27

The gray image is a code over GF(2) with n=152, k=14 and d=56.
This code was found by Heurico 1.16 in 0.898 seconds.