The generator matrix

 1  0  0  1  1  1  2  4  1  1  0 14  1  1  1  4  1 14  2  1  1  1  6  1  1  8  8  1  1  0  1  0  1  1  1  1  2 14  1  2  8  1  1
 0  1  0  2  1 11  1  6 14  9  1  1 15  6  7  1  8  1 10  4  5 15  1  0  1  1  4 10  5  1 10  1  8 15 15  3  6  1  8  1  2  8  0
 0  0  1  1  3  4  5  1  6  2  9  0  5  3 14  2  6 15  1  3  0  7  5 10 13  6  1  9  1 14  8  3  3  1 11  4  1  0  1  2  1  4  0
 0  0  0  4  0  0 12 12  4 12  8  4 12 12  8 12  8  0  0  4 12 12  4 12 12  0 12  8  8 12  0  8  8  4  8  8  8  8  8 12  8  4  0
 0  0  0  0  4  8  8  8  8  0  0  0  4  4  8 12 12  0  4  8 12  0  4  8  4 12  4 12  8  4  8  4  0  8  4  0  4 12  4 12  8  4  0

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

Homogenous weight enumerator: w(x)=1x^0+101x^36+494x^37+1271x^38+2678x^39+4811x^40+7770x^41+9909x^42+10972x^43+10847x^44+7698x^45+4515x^46+2648x^47+1140x^48+438x^49+127x^50+52x^51+24x^52+16x^53+18x^54+2x^55+4x^56

The gray image is a code over GF(2) with n=344, k=16 and d=144.
This code was found by Heurico 1.16 in 23.2 seconds.