The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+23x^34+26x^35+97x^36+214x^37+207x^38+674x^39+805x^40+1390x^41+1347x^42+1390x^43+797x^44+674x^45+188x^46+214x^47+77x^48+26x^49+19x^50+9x^52+5x^54+5x^56+3x^58+1x^60

The gray image is a code over GF(2) with n=336, k=13 and d=136.
This code was found by Heurico 1.16 in 0.8 seconds.