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  2  1  1  1  1  1  1  1  1  1  4  1  1  2  2  1  1  1  1  1  2  1  1  1  1  1  1  4  1
 0 12  0 12  0 12  0  4  8 12  0 12 12  0  8  4  8  4  0 12  0 12  8  4  8 12  4  0 12  0 12  0  8 12  4 12  8  4  0  8  0  8  0  8  0 12  0  0  8  8 12 12  8 12
 0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  0  8  8  0  0  8  0  8  8  0  0  8  8  8  0  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  0  8  8  8  0  0  0  0
 0  0  0  8  0  0  0  8  0  0  0  8  0  0  0  8  0  0  8  8  8  0  8  8  8  8  0  8  8  8  0  0  8  8  0  8  8  8  0  0  8  8  0  0  8  0  8  8  8  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  0  8  8  0  8  0  0  8  8  0  8  0  0  8  8  0  8  0  8  8  8  0  0  0  8  8  0  0  8  8  0  8  0  8  8  0  0
 0  0  0  0  0  8  0  8  0  8  8  0  0  8  8  0  8  8  0  0  8  8  0  8  8  8  0  8  8  8  8  0  8  0  8  8  8  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  8  0
 0  0  0  0  0  0  8  0  8  0  8  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  8  0  0  0  0  8  8  8  8  0  8  8  8  8  8  8  8  0  0  0  8  0  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+72x^48+60x^50+32x^51+190x^52+352x^53+700x^54+352x^55+128x^56+32x^57+52x^58+40x^60+20x^62+6x^64+10x^68+1x^96

The gray image is a code over GF(2) with n=432, k=11 and d=192.
This code was found by Heurico 1.16 in 0.198 seconds.