The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+19x^34+32x^35+120x^36+218x^37+458x^38+1144x^39+2564x^40+3312x^41+6066x^42+4918x^43+6061x^44+3394x^45+2562x^46+1038x^47+437x^48+230x^49+103x^50+34x^51+26x^52+12x^53+3x^54+2x^55+6x^56+2x^57+4x^58+1x^60+1x^70

The gray image is a code over GF(2) with n=344, k=15 and d=136.
This code was found by Heurico 1.16 in 7.6 seconds.