The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+235x^36+480x^38+48x^39+885x^40+688x^41+2082x^42+2336x^43+2888x^44+2336x^45+2156x^46+688x^47+845x^48+48x^49+388x^50+186x^52+76x^54+13x^56+2x^58+2x^60+1x^68

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 60.6 seconds.