The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  2  2  4  2  1  0  1  4  1  1  2  1  2  1  1  4  4  1  1  1  1  2
 0 12  0 12  0 12  0 12  0 12  8  4  0 12  0  8 12  4 12  0  0 12  4 12 12 12 12 12  0  4  0 12 12 12 12  4 12  0  8 12  8  4  8  4 12  8
 0  0  8  0  0  0  0  0  0  0  8  0  8  0  0  8  0  0  0  8  0  8  8  8  8  0  8  0  8  8  8  0  0  8  0  0  8  0  0  0  0  0  0  8  8  8
 0  0  0  8  0  0  0  0  0  0  0  8  0  8  0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  8  0  0  0  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  8  8  0  0  8  0  8  8  8  8  8  8  0  8  8  8  0  0  0  0  0  8  0  0  0  8  8  0  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  0  0  8  8  0  8  8  0  8  0  8  8  0  8  8  0  8  0  8  8  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  0  0  8  8  0  8  0  0  0  8  8  8  8  0  8  8  0  0  0  0  0  8  8
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  0  0  8  8  0  8  0  8  8  0  0  8  8  0  8  8  8  8  0  0  8  0  8  0  8
 0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  8  0  0  0  8  0  8  8  8  0  8  0  8  0  8  0  8  8  0  8  0  8  8  8  0  8  8  0  8  0  8
 0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  0  0  8  8  0  8  0  8  0  0  0  8  0  0  0  8  8  8  8  8  0  8  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+157x^36+92x^38+16x^39+422x^40+176x^41+394x^42+1168x^43+720x^44+4784x^45+568x^46+4784x^47+700x^48+1168x^49+388x^50+176x^51+394x^52+16x^53+92x^54+134x^56+2x^58+24x^60+7x^64+1x^68

The gray image is a code over GF(2) with n=368, k=14 and d=144.
This code was found by Heurico 1.16 in 5.29 seconds.