The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+46x^47+162x^48+310x^49+888x^50+1188x^51+1949x^52+2332x^53+2750x^54+2322x^55+1930x^56+1150x^57+844x^58+254x^59+141x^60+26x^61+24x^62+24x^63+4x^64+20x^65+4x^66+6x^67+2x^68+2x^69+2x^70+3x^72

The gray image is a code over GF(2) with n=432, k=14 and d=188.
This code was found by Heurico 1.16 in 2.96 seconds.