The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  2  1  1  1  1  2  4  0  2  1  1  1  4  2  1  1  1  1  4  2  1  1  2  1  1  1
 0 12  0 12  0 12  0 12  0 12  8 12  0 12 12  8 12  4 12 12  4  0  0 12 12  4 12  0  8 12 12 12  0  0  8  4 12 12  8  8 12  0  0  0
 0  0  8  0  0  0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  0  8  0  0  0  0  8  8  0  0  8  0  0  0  8  8  8  0  0  8  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  0  0  0  8  0  0  8  8  0  0  0  8  8  8  0  8  8  0  8  0  8  8  8  8  0  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  0  8  8  0  8  8  0  8  8  0  0  0  8  8  0  8  8  8  0  0  0  0  0  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  0  8  8  8  0  8  8  0  0  8  0  8  0  8  8  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  8  0  0  8  8  8  0  8  0  8  8  0  0  0  8  8  8  0  8  8  0  0  8  8  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  0  0  8  8  0  0  8  8  8  0  0  0  0  0  8  8  8  0  0  8  0  8  0  8  0  0  8  8  8  0
 0  0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  8  0  0  0  8  8  0  8  0  8  0  0  8  8  8  8  0  8  8  0  8  0  8  8  8  0

generates a code of length 44 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+60x^32+55x^34+8x^35+138x^36+96x^37+174x^38+296x^39+375x^40+1144x^41+748x^42+4600x^43+1028x^44+4600x^45+742x^46+1144x^47+327x^48+296x^49+212x^50+96x^51+98x^52+8x^53+82x^54+21x^56+24x^58+10x^62+1x^66

The gray image is a code over GF(2) with n=352, k=14 and d=128.
This code was found by Heurico 1.16 in 4.2 seconds.