The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1  1 10  1  1  0  1  1  1  6  1  1 10 12  1  1  1  0  1  1  6  1  1  1  1 12  2 10  2  1  1  6  2  2  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 15 12  1  9 10  1  0  3  5  1  6 15  1  1  3  9 15  1 12  0  1 10  5  6  9  1 10  1  0  6 15  1 12  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  0  0  0  8  8  8  8  0  0  8  8  0  8  0  0  0  8  0  8  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  0  8  0  8  8  8  8  8  0  0  8  8  0  8  8  0  0  0  8  8  8  0  8  0  0  0  8  8  0  8  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  0  8  0  8  8  8  8  0  8  8  0  0  8  0  0  0  0  0  8  0  8  0  0  0  8  8  8  8  0  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  8  8  8  0  8  0  0  8  0  8  8  0  8  8  8  0  0  8  8  8  0  8  8  0  8  8  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  8  8  0  0  0  8  8  0  8  8  8  8  8  0  8  8  0  0  0  0  8  8  8  0  0  0  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  0  8  0  8  8  0  8  8  8  0  8  8  0  8  0  8  8  0  8  0  0  0  0  8  0  0  0  8  8  8  8  8  0  0  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  0  8  8  0  0  8  0  8  0  8  8  0  0  0  8  0  8  0  8  0  8  8  8  0  8  0  0  8  8  8  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+35x^44+46x^45+83x^46+198x^47+232x^48+900x^49+1196x^50+2692x^51+3580x^52+4760x^53+5126x^54+4944x^55+3633x^56+2836x^57+1174x^58+828x^59+156x^60+154x^61+67x^62+42x^63+29x^64+8x^65+20x^66+12x^68+12x^70+1x^72+2x^74+1x^76

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 10.5 seconds.