The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+202x^39+422x^40+610x^41+480x^42+746x^43+520x^44+528x^45+320x^46+194x^47+40x^48+10x^49+8x^51+3x^52+4x^53+5x^56+2x^59+1x^60

The gray image is a code over GF(2) with n=344, k=12 and d=156.
This code was found by Heurico 1.16 in 11.1 seconds.