The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+106x^36+156x^37+620x^38+584x^39+1181x^40+1892x^41+2238x^42+2928x^43+2200x^44+1924x^45+1193x^46+552x^47+428x^48+124x^49+165x^50+32x^51+47x^52+7x^54+2x^56+1x^58+3x^60

The gray image is a code over GF(2) with n=344, k=14 and d=144.
This code was found by Heurico 1.16 in 3.03 seconds.