The generator matrix

 1  0  0  1  1  1 14  1  1  1  1  0  0  1  4  2  1  4  0
 0  1  0  1  6 15  1  5  2  2 11  1  0  6  1  1  1 10  2
 0  0  1  1 11  2  3  3  6  1  4  1  1 12  2  7 15  1  1
 0  0  0 12  0  0  0  8  8 12 12  4  4  4 12  4  4 12  0
 0  0  0  0 12  4  4  8 12 12  4  0 12  4  4  4 12  0 12

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

Homogenous weight enumerator: w(x)=1x^0+220x^14+616x^15+2367x^16+6844x^17+13460x^18+18368x^19+13710x^20+6856x^21+2292x^22+568x^23+176x^24+28x^25+28x^26+2x^28

The gray image is a code over GF(2) with n=152, k=16 and d=56.
This code was found by Heurico 1.16 in 7.2 seconds.