The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  0  1  2  1  8  1  1  1  2  1  1  1  1 12  1  1  1  2  2 12  1  1  1  1  8  1
 0  2  0  6  4 14 12  2  0  6 12 10  8 14  0  6  2  2 12 14 10  2 12  4 10 10  6  4  4  6  2 10  4 10  6 12  2  2  8 12 12  2  0
 0  0 12  0  4  4  0  4  0  8  0  8 12 12  8  8 12  0 12 12  8  4  0  4  0  0  4  4  4  8  0 12  8  8  8  4  0 12  4  0 12 12  0
 0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  0  8  8  8  8  0  0  0  0  8  8  8  8  0  8  0  0  0  0  8  0  8  8  0
 0  0  0  0  8  0  0  8  8  8  8  0  8  0  0  8  8  8  0  0  8  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  8  0  0  8  8  0  0
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  0  8  8  8  8  0  0  8  0  8  8  0  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  0  8  8  0  0  0  8  8  0  8  0  8  0  0  0  8  8  0  8  0  8  8  0  0  8  8  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+56x^36+78x^37+200x^38+230x^39+618x^40+826x^41+1406x^42+1336x^43+1556x^44+826x^45+510x^46+208x^47+173x^48+54x^49+47x^50+16x^51+28x^52+8x^53+10x^54+2x^55+2x^58+1x^66

The gray image is a code over GF(2) with n=344, k=13 and d=144.
This code was found by Heurico 1.16 in 0.85 seconds.