The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+306x^49+844x^50+1842x^51+1915x^52+2664x^53+2102x^54+2172x^55+1522x^56+1624x^57+698x^58+372x^59+168x^60+88x^61+30x^62+12x^63+9x^64+6x^65+6x^66+2x^67+1x^68

The gray image is a code over GF(2) with n=432, k=14 and d=196.
This code was found by Heurico 1.16 in 2.05 seconds.