The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+64x^34+128x^35+213x^36+452x^37+804x^38+1314x^39+2406x^40+3632x^41+4701x^42+5308x^43+4683x^44+3778x^45+2532x^46+1188x^47+689x^48+414x^49+194x^50+124x^51+63x^52+42x^53+24x^54+2x^55+8x^56+2x^57+1x^58+1x^60

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 12.7 seconds.