The generator matrix

 1  0  1  1  1  6  1  1 12  1 14  1  1  8  1  1  1  6  4  1  1  2  1  1  1  4  1  1  1  1 14  0 12  1  1  1  0  1 12  1  2  1  1
 0  1 11  6 13  1  0  7  1  6  1  5 10  1  4 11  9  1  1  0  3  1 14 13  4  1  1 10  5 10  1  1  1 12 11  1  1 15  2 11  6 10  3
 0  0 12  0  4  0  0  4  0  0  4  8  8  4  8  0 12  4  0  4 12  8  4  8  4  4  8  4  4  0  0  0 12 12 12  8  4  0 12 12  4  0  4
 0  0  0 12  0  0 12  8  0  8  8  0  8  0  4  4 12  4 12 12  4 12  0  4  0  0 12  4  4  0 12  8 12  4  8  4 12  8 12  8 12  0  4
 0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  8  0  8  0  0  0  0  0  8  8  0  8  0  8  0  0  0  8  0  0  0  0  8  8  8  0
 0  0  0  0  0  8  0  8  0  0  0  0  8  8  8  0  8  8  8  0  8  0  8  8  0  8  8  8  0  8  0  8  8  0  8  0  8  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  8  0  0  0  8  0  8  0  8  8  0  8  8  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+226x^36+100x^37+634x^38+1032x^39+2358x^40+3700x^41+5568x^42+5656x^43+5476x^44+3788x^45+2308x^46+984x^47+561x^48+92x^49+176x^50+8x^51+66x^52+18x^54+16x^56

The gray image is a code over GF(2) with n=344, k=15 and d=144.
This code was found by Heurico 1.16 in 17.2 seconds.