The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+188x^49+373x^50+886x^51+924x^52+1312x^53+1094x^54+1212x^55+839x^56+778x^57+258x^58+166x^59+55x^60+44x^61+33x^62+8x^63+4x^64+14x^65+1x^66+1x^68+1x^78

The gray image is a code over GF(2) with n=432, k=13 and d=196.
This code was found by Heurico 1.16 in 0.734 seconds.