The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^36+248x^37+636x^38+1352x^39+1801x^40+2814x^41+2761x^42+2774x^43+1753x^44+1214x^45+552x^46+222x^47+88x^48+74x^49+14x^50+2x^51+9x^52+2x^53+4x^54+2x^55+2x^56+1x^58

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 1.91 seconds.