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

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

Homogenous weight enumerator: w(x)=1x^0+264x^48+72x^50+674x^52+512x^53+1136x^54+512x^55+591x^56+72x^58+216x^60+39x^64+6x^68+1x^88

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 66 seconds.