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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+54x^44+40x^46+12x^47+60x^48+48x^49+51x^50+88x^51+40x^52+624x^53+2093x^54+624x^55+52x^56+80x^57+41x^58+40x^59+26x^60+16x^61+36x^62+4x^63+15x^64+33x^66+8x^68+6x^70+3x^74+1x^86

The gray image is a code over GF(2) with n=432, k=12 and d=176.
This code was found by Heurico 1.16 in 0.503 seconds.