The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  6  1  1  0  1 12  1  1  1 10  1  1  1  0  1  1  6  1  1  1  0  1 10  1  1  1  6  1  1 12  1  1 10  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  6  5  1  9  1 12 10 15  1  6  0  3  1 12 10  1  5  0  6  1 15  1  9 12  0  1 12 15  1  3 10  1  3  6  5  3
 0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  0  8  0  8  0  8  8  0  8  0  0  0  0  0  8  0  8  8  0  8  0  8  0  0  0  8  0  8  8  8  0  8  0
 0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  0  8  8  0  0  8  8  0  0  8  0  0  0  8  8  0  8  0  0  8  0  8  8  8  8  0  8  8  8  0  8  0
 0  0  0  0  8  0  0  0  0  8  8  0  8  8  0  0  8  8  8  8  0  8  8  0  0  8  8  0  0  0  8  8  0  0  8  0  0  0  0  8  0  8  0  0  8  0  8  8  0  0  8
 0  0  0  0  0  8  0  0  8  0  8  8  0  0  8  8  8  0  0  8  0  8  8  0  8  0  0  8  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  0  0  0  0  8  8  0  0
 0  0  0  0  0  0  8  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  0  0  8  0  8  8  8  0  8  0  0  8  0  0  0  8  0  8  0  8  0  8  8  8  0  0  0  8  0
 0  0  0  0  0  0  0  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  0  8  8  8  8  0  8  0  0  8  0  0  0  8  8  0  8  0  8  0  0  0  0  0  8  8  8  8  8

generates a code of length 51 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+126x^44+104x^45+304x^46+656x^47+1178x^48+2072x^49+2240x^50+3040x^51+2282x^52+2072x^53+1104x^54+656x^55+342x^56+104x^57+64x^58+18x^60+13x^64+6x^68+2x^72

The gray image is a code over GF(2) with n=408, k=14 and d=176.
This code was found by Heurico 1.16 in 3.21 seconds.