The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+155x^36+28x^37+212x^38+200x^39+1035x^40+776x^41+2408x^42+1544x^43+3646x^44+1568x^45+2496x^46+792x^47+928x^48+184x^49+248x^50+24x^51+79x^52+4x^53+12x^54+35x^56+8x^60+1x^64

The gray image is a code over GF(2) with n=352, k=14 and d=144.
This code was found by Heurico 1.16 in 14.8 seconds.