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

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

Homogenous weight enumerator: w(x)=1x^0+211x^44+568x^46+4x^47+885x^48+156x^49+1474x^50+1556x^51+3960x^52+4428x^53+6258x^54+4428x^55+4065x^56+1556x^57+1506x^58+156x^59+811x^60+4x^61+422x^62+224x^64+76x^66+18x^68+1x^88

The gray image is a code over GF(2) with n=432, k=15 and d=176.
This code was found by Heurico 1.16 in 22.7 seconds.