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  2  1  2  2  1  1  2  1  1  1  1  1  1  1  1  2  2  1  1  1
 0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  8  0  8  8  8  8  0  8  8  8  0  8  0  8  0  8  0  8  0
 0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  0  0  8  0  8  0  0  8  0  8  8  0  8  8  0  0  8  0  0  0  8  0
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  0  8  8  8  8  8  0  0  0  0  8  8  0  0  8  8  0  8  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  0  0  8  0  8  8  0  8  0  0  8  0  8  0  8  8  8  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  8  0  8  8  8  0  0  8  8  8  8  0  8  8  0  8  8  8  8  8  8  8  0  8  8  8  8
 0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  0  8  8  0  8  8  0  0  8  8  0  8  8  0  8  8  0  0  0  0  0  0  0  8  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  8  0  8  0  0  8  0  0  0  0  8  0  8  8
 0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  0  8  0  8  0  0  8  8  8  0  0  0  8  8  8  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+37x^34+68x^36+8x^37+65x^38+48x^39+53x^40+120x^41+47x^42+3232x^43+48x^44+120x^45+42x^46+48x^47+47x^48+8x^49+41x^50+28x^52+21x^54+11x^56+2x^58+1x^74

The gray image is a code over GF(2) with n=344, k=12 and d=136.
This code was found by Heurico 1.16 in 0.491 seconds.