The generator matrix

 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  4  1  1  0  1  1  1  1  1  4  1  2  0  2  4  1  1  1  2  2  1  1  2  2  1
 0 12  0 12  0 12  0 12  0  4  8  0 12 12  4  0  8  0  8  0 12 12  0 12  4 12 12  4 12 12 12  4  4  0  8  8  8  0 12 12 12  4 12 12  4  0  4 12  4  0  4 12  0  0
 0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  0  8  0  8  8  0  0  8  0  8  0  8  0  0  0  0  0  0  8  8  8  8  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  8  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  8  8  8  0  8  8  8  0  8  0  0  8  0  8  8  8  8  8  0  0  8  8  8  0  0  8  0  0  0  0  8  0  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  8  0  8  8  0  0  0  0  8  8  8  8  0  8  8  8  0  0  0  8  8  0  8  8  0  8  0  0  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  0  0  0  0  8  0  0  8  0  0  8  8  0  8  0  8  8  8  8  8  8  8  0  8  0  0  0  8  8  0  8  8  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  8  8  8  0  8  0  8  8  8  8  8  8  8  0  0  0  0  8  0  8  0  8  0  8  0  8  0  8  0  0  0  8  0  8  8  0  8  0
 0  0  0  0  0  0  0  8  0  8  0  0  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  8  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  0  0  0  0  0  8  0  8  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  0  0  0  8  0  0  8  8  8  8  0  0  8  0  0  8  8  0  8  8  8  0  0  8  0  8  0  8  8  0  0  8  8  0  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+56x^44+14x^45+67x^46+84x^47+122x^48+228x^49+119x^50+708x^51+619x^52+1520x^53+1139x^54+1548x^55+628x^56+700x^57+101x^58+204x^59+78x^60+98x^61+70x^62+16x^63+25x^64+25x^66+7x^68+11x^70+3x^74+1x^78

The gray image is a code over GF(2) with n=432, k=13 and d=176.
This code was found by Heurico 1.16 in 1.57 seconds.