The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  2  1  1  2  1  1  1  1  1  2  1  2  2
 0 12  0 12  0 12  0 12  8  4  0 12  4  0  8 12  8 12  8  4  0  0 12  4  0  8  0  8 12 12  4  4  0  0  8  0  0  0  8  0  8  8 12 12 12 12  4 12  4 12 12  4 12 12
 0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  0  8  8  0  8  0  8  0  0  0  8  8  0  0  0  0  0  8  0  8  0  8  0  0  8  8  8  0  0  0  8  8  8  0  0  0  8  8  8
 0  0  0  8  0  0  0  0  0  8  0  8  0  0  0  8  0  0  0  8  8  8  0  8  0  8  0  8  0  8  8  0  8  0  8  8  0  8  0  0  8  8  0  8  8  8  8  0  0  0  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  0  8  0  8  0  8  0  8  8  8  0  0  8  0  8  0  8  0  0  0  8  8  8  0  0  8  0  8  0  8  0  8  8  8  8  0  8  0  8
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  8  8  0  0  8  8  8  0  8  8  0  0  8  0  8  0  0  0  0  0  8  0  8  0  0  0  8  0  8  8  0  0  8  8  0  0  8
 0  0  0  0  0  0  8  0  8  0  8  8  8  0  0  0  8  8  0  8  8  8  0  0  8  0  8  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  8  8  8  8  8  0  8  0  0  8  0  8
 0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  0  0  8  0  0  8  8  8  0  8  8  8  8  8  0  8  8  8  8  8  8  0  0  8  0  8  8  0

generates a code of length 54 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+287x^48+64x^50+208x^52+2944x^54+305x^56+64x^58+176x^60+43x^64+3x^72+1x^96

The gray image is a code over GF(2) with n=432, k=12 and d=192.
This code was found by Heurico 1.16 in 16.2 seconds.