The generator matrix

 1  0  1  1  1 14  1  2  1 12  1  1  1  1  8  1  1  4  1  1  1  1  0 12  6 10  6 10  0  8  1  1  1  1 14  8  2 14 10  6  1  1  0  1  1  1  6  1  6  1  4  1  1
 0  1 11  6 13  1 12  1  7  1 14  5  8  3  1  2  9  1  4  1 10 15  1  1  1  1  1  1  1  1  0 10 13 11  1  1  1  1  1  1 14  8  2  3  0 11  1  4  1  5  1 14  0
 0  0 12  0  4  4  8  4  4  8  4  0 12  8 12  4  0 12 12 12  8  8  0  8  0  0  0  0 12  4  0  8  4 12 12 12 12  8  4  8 12 12  0  0  4  8  8 12  4  0  0  4  0
 0  0  0  8  0  8  8  8  8  0  0  8  0  8  0  8  0  0  8  8  0  0  8  8  0  8  0  8  8  8  8  0  8  0  0  8  0  8  0  0  8  0  0  0  8  8  8  0  8  8  8  8  0
 0  0  0  0  8  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  0  0  8  0  8  8  0  8  0  0  0  8  8  0  0  8  8  0  0  8  0  8  8  0  8  0  0  0  0  8  0  0

generates a code of length 53 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+62x^48+222x^49+393x^50+516x^51+596x^52+606x^53+561x^54+492x^55+348x^56+194x^57+68x^58+10x^59+12x^60+4x^63+2x^64+1x^66+2x^67+2x^68+2x^69+1x^72+1x^78

The gray image is a code over GF(2) with n=424, k=12 and d=192.
This code was found by Heurico 1.16 in 0.262 seconds.