The generator matrix

 1  0  1  1  1  4  1  1  2  1 10  1  1 10  1  1  4  6  1  1 14  1  1  1  1 10  8  1  1  2  1  1  1  4  1  1  4  1  4 10  1  1  1
 0  1  1  0 11  1 14 15  1  1  1  2  8  1  6  3  1  1  1  0  1 13  6  5 15  1  2  4  9  8 14  6 10 12  0 14  2  4  1  1  1 11  0
 0  0  2  6  0  2  8  2  6 12 12  2  0 10  0  8  2  4 14  6 12  2  2 14  6  6  2  0  8 14 10 14  6  2  8  4  6  6  2  2  2  8  4
 0  0  0 12  0  0  0  8  8  8  8  4  4 12  4 12 12  4  4  0  4  4  0 12  8  4  4  8  8 12 12  8  0  0  8 12  8  4  8  8  0  4 12
 0  0  0  0 12  8  4 12 12  0  4  4  8  8  4  4 12  0  0  8  4 12 12 12  0  4  8 12  0 12  8  4 12 12  4 12  4  4  4  0 12  0  8

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

Homogenous weight enumerator: w(x)=1x^0+48x^36+232x^37+753x^38+1448x^39+2094x^40+4040x^41+4911x^42+5994x^43+4518x^44+4190x^45+2354x^46+1170x^47+548x^48+268x^49+103x^50+38x^51+20x^52+22x^53+7x^54+6x^55+3x^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 7.8 seconds.