The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  8  2  2  1  8  2  1  1  2  1  1  1  4  1  1  1 12 12  1  8  1  1  8  2  2
 0  2  0  6  0  6  0  2  4  6 12 10 12  2  4 14  6  2  2  6 14 12  2  2  6 14  2 10  2  0  2 12  6  0  2  2 12  8  2 10  2  6  0
 0  0 12  0  0  4  4  4  4  0  8  4 12  8  0  4  4  8 12  8  8  0  8  4  0  8  0  4  8  8  4  8 12  0 12  0 12  4  4  8 12 12  8
 0  0  0 12 12  4  4  0  8  8  8  4 12 12  4  8 12  8  8  8 12  0  4  8  8  4  4 12 12 12  0  0  4  8 12  8  0 12  0  0  8 12  0
 0  0  0  0  8  0  0  0  8  8  8  0  8  0  0  0  8  8  0  8  0  8  8  0  8  8  0  0  8  8  0  8  8  8  0  0  0  0  0  0  0  0  8
 0  0  0  0  0  8  0  0  0  0  8  0  8  0  0  8  8  0  0  0  8  0  8  8  8  0  0  8  8  8  8  8  0  0  0  8  0  0  8  8  0  8  0
 0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  0  0  0  8  8  0  8  8  0  8  8  0  0  0  8  0  8  0  0  0  8  8  8  8  0  8  8  0
 0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  8  8  8  0  8  8  8  8  0  0  8  8  0  0  0  0  8  0  0  0  8  8  0  0  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+119x^34+12x^35+426x^36+188x^37+850x^38+1076x^39+2731x^40+3516x^41+4994x^42+4748x^43+5335x^44+3540x^45+2622x^46+1052x^47+841x^48+180x^49+330x^50+24x^51+126x^52+40x^54+11x^56+4x^58+1x^60+1x^66

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 12.4 seconds.