The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  0  1  1  1  6  1  1  1 10  1  1  1 12  0  1  6  1  1  1  1  1 10 10 12  1  1  1  1  1  1
 0  1  3  6  5  1 12 15  1 10  9  1  0  1  3  6  5  1 12  9 10  1  0  9 15  1  1  3  1  6  5 12 10  6  1  1  1  5  9  5  5  0  0
 0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  0  8  8  8  8  0  8  0  0  8  0  8  8  8  8  8  8  0  0  8  0  0  8  0  8  8  0  0
 0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0  0  0  0  8  8  8  8  8  0  0  8  8  0  0  8  0  8  0  8  8  8  0  0  0
 0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  8  0  0  8  8  0  0  0  0  8  0  8  0  0  8  8  8  8  8  8  8  8  8  0  0
 0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  0  8  0  8  8  0  0  0  8  8  0  8  0  8  8  8  0  0  0  8  0  0  0  8  0  0  0
 0  0  0  0  0  0  8  8  0  8  0  8  8  8  8  8  8  8  8  0  8  0  0  0  8  0  8  0  0  0  0  8  0  8  8  0  0  0  8  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+20x^36+32x^37+161x^38+240x^39+717x^40+800x^41+1545x^42+1184x^43+1537x^44+800x^45+708x^46+240x^47+147x^48+32x^49+12x^50+2x^52+3x^54+7x^56+3x^58+1x^60

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 0.512 seconds.