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

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

Homogenous weight enumerator: w(x)=1x^0+241x^36+408x^37+1029x^38+1356x^39+2521x^40+3436x^41+4872x^42+5084x^43+5066x^44+3284x^45+2495x^46+1332x^47+853x^48+420x^49+263x^50+36x^51+49x^52+4x^53+12x^54+5x^56+1x^58

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 10.7 seconds.