The generator matrix

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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+58x^36+64x^37+158x^38+242x^39+478x^40+730x^41+1130x^42+2292x^43+3525x^44+4824x^45+5631x^46+4932x^47+3694x^48+2316x^49+1076x^50+664x^51+380x^52+248x^53+164x^54+58x^55+42x^56+10x^57+26x^58+4x^59+13x^60+7x^62+1x^64

The gray image is a code over GF(2) with n=368, k=15 and d=144.
This code was found by Heurico 1.16 in 13.3 seconds.