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  6  2  1  1  2  6  2  1  1  1  1  1  1  2  4  4  2  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 14  8  4  1  1  3  0 15 14  6 11  1  1  2  1  8
 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  4  4  4 12  8  8  8 12  0 12  4  0 12  0  4 12  4
 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  0  8  0  0  0  0  0  8  8  8  0  0  0  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  0  8  0  0  8  0  8  0  8  8  8  0  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+60x^49+303x^50+286x^51+630x^52+384x^53+850x^54+374x^55+646x^56+208x^57+185x^58+74x^59+64x^60+16x^61+3x^62+2x^63+2x^64+4x^65+2x^66+1x^72+1x^78

The gray image is a code over GF(2) with n=432, k=12 and d=196.
This code was found by Heurico 1.16 in 0.273 seconds.