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  2  2  4  2  4  2  2  4  1  1  8  2  4  2  1  4  0  2  2  4  1  1  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  8  4 12 12  0  4  8  8  0 12  4  0  0  4  8  0 12  8  0  8  8 12  4 12  8  4  4  8  8  8  8  0  4  4  0 12  0
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4 12  0  8 12 12  8  0  0 12  8  4  0  4  4  0  8  8 12  4  4  4 12  0  8  4  4  0  4  8  8  0  4 12  0 12  0  0
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  0 12 12  0  8  0  0 12  4  0  8  4  0  4  8  4  4  8  4  4  8  8  4  4  8 12 12  4  0  0 12  4  0  0 12  8  0  0
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  0  8  8  0  8  0  8  0  0  8  0  0  0  8  0  8  8  8  8  0  0  0  8  8  8  0  0  8  8  0  8  0  0  8  8  8  8  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  8  0  8  0  8  8  8  8  0  8  8  8  0  8  8  0  8  8  8  8  8  0  8  0  8  0  8  8  0  8  8  0  0  0  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  0  0  0  8  0  0  8  8  8  0  8  8  8  8  0  8  8  0  0  0  8  8  0  0  8  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  8  8  0  8  0  0  8  0  0  0  0  8  8  8  8  8  0  8  0  8  8  8  8  0  0  8  8  8  8  0  8  0  0  8  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+54x^44+76x^45+144x^46+208x^47+334x^48+440x^49+702x^50+1190x^51+1640x^52+2196x^53+2391x^54+2222x^55+1768x^56+1154x^57+711x^58+410x^59+234x^60+198x^61+114x^62+58x^63+57x^64+30x^65+24x^66+8x^67+8x^68+2x^69+7x^70+3x^74

The gray image is a code over GF(2) with n=432, k=14 and d=176.
This code was found by Heurico 1.16 in 5.87 seconds.