The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  4  2  1  1  2  2  8  2  8  2  1  0  1  0  1  2  1  0  2 12  2
 0  2  0  0  0  2  6 14  8  8 14  6 12 10  8 14  6 14 12  4  2  2  0 10  0  6 10  2  2  4 10  6 12  4  2  2 10  2  4  0  2  2
 0  0  2  0  2  2 10  0 12 14  8  2 12 12  2 10  6  4 14 12 10 12  6  4  4  8 10  6  2  0  4  4  2  4  6  8 14  4 12  2  4  4
 0  0  0  2  2  8 10  2  4  0 14 12  2  0  6  8  6  4  8  4  6  6  0  2  6 14 12  4  6  2 12  6 14  0 14  2 14  8  2 10 12  0
 0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  8  8  8  8  8  0  8  0  0  0  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+210x^36+516x^37+787x^38+1330x^39+1754x^40+2534x^41+2221x^42+2670x^43+1764x^44+1098x^45+683x^46+398x^47+205x^48+138x^49+47x^50+18x^51+2x^52+2x^53+6x^54

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 4.08 seconds.