The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  2 12  1  1  2  0  1  1  1  2  1  1  1 12  1  1  2  1  1  1  0  1 12  1  1  0  2  1  2  0  1  1  0  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  4  6 10  0  6  2 12 10  2  0 12  6  2  6 10  0 10  6  6  8  2 14 12  6  6  0  0  2 14  2 12 12  2 10 10  6  2  6 10  2  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  0  8  8  0  0  0  8  8  8  8  0  0  8  0  8  0  8  8  8  0  0  0  0  8  0  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  8  0  8  8  8  8  8  0  8  8  0  0  0  0  8  8  0  0  0  0  8  0  0  8  0  8  8  8  0  8  8  0  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  0  0  8  0  0  8  0  8  0  8  8  8  0  8  8  0  8  8  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  0  0  8  8  0  8  0  0  0  8  8  8  8  8  8  0  8  0  8  0  0  0  0  8  0  8  0  0  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  0  0  8  0  8  8  0  8  8  8  8  8  8  0  8  8  0  8  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  8  8
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  8  8  0  8  0  0  0  0  0  0  8  8  0  8  0  8  0  8  8  8  8  0  8  0  0  8  8  0  0  0  8  8  8  8  0  0  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  8  8  0  0  8  0  8  0  8  0  8  8  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  0  0  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+61x^44+12x^45+76x^46+140x^47+297x^48+432x^49+496x^50+1456x^51+1334x^52+3080x^53+1672x^54+3080x^55+1307x^56+1456x^57+496x^58+432x^59+238x^60+140x^61+76x^62+12x^63+54x^64+30x^68+5x^72+1x^76

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 4.66 seconds.