The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 14  2  1  1  8  1  1  1  4  1  1 14  1  1  0 10  1  1  1  8  1  1  1  4  2  1  1 12  1  1  1
 0  1 11  6 13  1 12  7  1 10  1  1  1  8  3  1  5 14 15  1  4  9  1  7  6  1  1 10  3  8  1  2  7  6  1  1 15 11  1  4 11  0
 0  0 12  0  4  0  0  4  8  8  4 12 12  4  8  4  8  4  0  4  4  0 12 12  0  8  8  8  8 12 12 12 12  0 12  4  0 12  0 12  4  8
 0  0  0  8  0  0  0  0  8  0  8  8  0  8  8  0  0  8  0  8  0  8  8  8  0  8  0  0  0  8  8  0  8  0  0  0  8  0  0  8  0  8
 0  0  0  0  8  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  8  8  0  8  8  8  8  8  8  8  8  0  0  8  8  8  8  8  8  0  8  0
 0  0  0  0  0  8  0  8  0  8  8  0  0  0  8  8  8  0  0  8  8  8  8  0  8  8  0  0  8  8  8  0  0  0  0  0  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  8  8  8  8  8  8  0  0  0  8  8  0  0  0  8  0  8  0  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+160x^36+128x^37+704x^38+1024x^39+2095x^40+2432x^41+3366x^42+2432x^43+2076x^44+1024x^45+638x^46+128x^47+117x^48+18x^50+26x^52+10x^54+3x^56+2x^60

The gray image is a code over GF(2) with n=336, k=14 and d=144.
This code was found by Heurico 1.16 in 41.1 seconds.