The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  2  2  1  0  1  1  0  1  2  1  2  1  1  2  4  1  1  1  2  0  1  1  1  1  4  1  1  2 12  4  1  4  2  1
 0  2  0  6  0 14  0 10  0  2  2 12 10  2  8 12  6 14 12  2  6 14  8  2  4  0  2 14  6  0 10  6 14 10  2 14  4 14  2  0  8 10  6 14  2  6  8  2  2  4 10  4 14  0
 0  0 12  0  0  0  4  8  0  4 12  4  4 12  0  8  8 12 12  8  4 12  4  0  0  0  4  0  4  8  4 12  0  0  8  4 12  8  0  0  8 12  8 12  4 12 12  0  0  0  8  4  0  0
 0  0  0 12  0  0  0 12  4  0 12 12  4  8  4 12  8  0  8 12 12  8  4  4  8  8  4  4  8 12  0  4  8  0  0  0  0 12  4  4  4  8  0 12 12  4 12  8  4  8 12 12  4  0
 0  0  0  0 12  4  4  4 12  8  4  8  0  4  8  4  0  0  4  8  8  0 12  4  4  0  0  8 12  0 12  0  4  0 12 12  8  4  8  0  0  8  4  8  4  4 12 12 12 12  8  4  8  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  0  8  0  8  0  8  0  0  0  8  8  0  8  8  0  0  0  8  8  8  0  0  8  0  8  0  0  8  8  8  0  8  8  8  8  8  0  8  0
 0  0  0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  8  0  8  0  0  0  8  8  0  0  8  8  8  8  0  8  8  8  0  8  0  0  8  0  0  0  0  8  0  8  0  8  0  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+67x^44+122x^45+184x^46+378x^47+497x^48+1054x^49+1647x^50+2472x^51+3472x^52+4124x^53+4623x^54+4220x^55+3626x^56+2552x^57+1523x^58+1008x^59+451x^60+294x^61+190x^62+106x^63+68x^64+42x^65+21x^66+8x^67+10x^68+4x^69+3x^70+1x^74

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 17.2 seconds.