The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  4  1  2  2  0  4  1  4  4  1  2  2  2  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  8  4 12 12  0  4  0  4  4  4 12  8  4  4  4 12  0 12 12  0  0  4 12  8  8  4
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4 12  0  8 12  8 12  4  0  0 12  0  4  0  8 12  4  4 12  0  4 12  8  0  0  8  0
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  0 12 12  0  8 12 12 12  4 12  8  8  0 12  0  8 12  0  4  0  4  0 12  0  4 12  4
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  0  8  8  0  8  0  8  8  8  0  0  8  0  8  8  8  8  8  0  0  0  8  8  0  0  8  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  8  0  8  0  8  0  0  0  0  8  8  0  0  0  0  8  0  8  8  8  8  0  8  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  0  8  8  0  0  0  8  0  0  8  8  8  8  8  0  0  0  0  8  0  8  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  8  8  0  8  0  8  0  0  8  8  8  0  0  8  8  8  8  0  0  0  0  8  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+68x^34+96x^35+169x^36+282x^37+327x^38+540x^39+996x^40+1752x^41+2563x^42+2830x^43+2572x^44+1810x^45+952x^46+534x^47+279x^48+238x^49+156x^50+90x^51+67x^52+12x^53+25x^54+6x^55+12x^56+2x^57+5x^58

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 4.26 seconds.