The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2  1 12  1  0  1  2  1  1  2  1  1  1 12  1  1  1  1  1  1  1  1  2  2  2  1
 0  2 12  6  0  6 12 10  0  6 12 10  0  6  2  6 10 10 12  2 12  2  0  6  6  0 10  0 10 12  2  6  6 10  0 12 12  8  6  6  6  6  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  0  8  0  0  8  8  8  8  8  8  0  8  0  0  8  8  8  8  0  8  0  0  0  0  8  8  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  0  0  0  8  8  0  0  8  8  8  0  8  0  8  0  8  0  8  8  8  8  8  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  0  8  8  0  8  0  0  8  8  0  8  0  0  0  8  0  8  8  8  0  8  0
 0  0  0  0  0  8  0  0  0  8  0  8  0  0  8  0  8  0  8  8  8  0  8  0  8  8  0  0  8  0  8  0  8  8  8  0  8  0  8  0  0  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  0  8  0  0  0  0  0  0  0  8  0  8  0  8  8  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  8  8  0  0  8  8  0  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  0  8  0  8  0  8  0  8  0  0  8  0  8  8  8  0  0  0  0  0  8  0  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+39x^34+40x^35+89x^36+248x^37+224x^38+624x^39+628x^40+2824x^41+1086x^42+4816x^43+1083x^44+2824x^45+617x^46+624x^47+206x^48+248x^49+55x^50+40x^51+27x^52+22x^54+12x^56+4x^58+1x^60+1x^62+1x^64

The gray image is a code over GF(2) with n=344, k=14 and d=136.
This code was found by Heurico 1.16 in 3.83 seconds.