The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+119x^36+12x^38+256x^40+112x^42+415x^44+1024x^45+4360x^46+1024x^47+399x^48+112x^50+205x^52+12x^54+107x^56+29x^60+4x^64+1x^72

The gray image is a code over GF(2) with n=368, k=13 and d=144.
This code was found by Heurico 1.16 in 1.39 seconds.