The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+123x^44+8x^45+346x^46+112x^47+692x^48+720x^49+1425x^50+2752x^51+2806x^52+5568x^53+3543x^54+5696x^55+2823x^56+2800x^57+1532x^58+640x^59+607x^60+120x^61+272x^62+16x^63+97x^64+33x^66+16x^68+15x^70+3x^72+2x^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 17.4 seconds.