The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+119x^44+20x^45+150x^46+128x^47+624x^48+496x^49+1488x^50+1152x^51+3301x^52+1528x^53+3196x^54+1152x^55+1567x^56+496x^57+512x^58+128x^59+206x^60+20x^61+30x^62+45x^64+21x^68+3x^72+1x^76

The gray image is a code over GF(2) with n=424, k=14 and d=176.
This code was found by Heurico 1.16 in 4.68 seconds.