The generator matrix

 1  0  1  1  1  6  1 12  1 10  1  1  1  1 14  1  1  8  1  1  1  6  4  1  1  1 14  1 12  2  1  8  1  1  1  6  8  6  1  1  1  1
 0  1 11  6 13  1 12  1  3  1  5 10  7  8  1 14  1  1 15  4 13  1  1 12  2  6  1  5  1  1  8  1  8  1 11  1  1  1  3 13  6  0
 0  0 12  0  4  0  0  8  0  8  8  0 12  4  4  4  4  4  0 12 12  8 12  8 12  0 12  0  8  4 12  4  4  4  4  8  8 12  0  0  0  0
 0  0  0  8  0  0  8  0  0  8  8  8  8  0  0  8  8  8  0  8  8  8  8  0  0  0  8  8  8  0  0  0  8  8  8  0  8  0  8  0  8  0
 0  0  0  0  8  0  8  8  8  0  0  0  8  0  8  0  0  0  8  0  0  8  0  8  8  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  8  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  0  0  8  0  0  0  0  8  8  8  0  0  8  8  8  8  0  8  0  0  0  0  0  0

generates a code of length 42 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+40x^36+84x^37+335x^38+588x^39+1254x^40+1002x^41+1649x^42+996x^43+1225x^44+572x^45+306x^46+78x^47+26x^48+2x^49+6x^50+11x^52+4x^53+7x^54+2x^55+3x^56+1x^58

The gray image is a code over GF(2) with n=336, k=13 and d=144.
This code was found by Heurico 1.16 in 0.53 seconds.