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  2  2  1  2  1  1  2  1  1  2  1  1  1  1  1  2  2  2  4  1  2  1  1
 0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  0  8  8  0  0  8  8  8  8  0  0
 0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  0  0  8  0  0  0  8  8  0  8  0  0  0  8  0  0  8  0  8  8  8  0  8  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  0  8  8  8  0  8  8  0  0  0  8  0  8  8  8  8  8  0  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  0  0  0  8  8  0  8  8  8  0  8  0  0  0  8  0  8  0  0  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  8  0  8  8  8  0  0  8  8  0  8  0  0  8  8  8  8  0  8  8  0  8  8  0  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  0  8  8  0  8  8  8  0  0  0  8  8  0  0  8  0  8  0  8  0  8  8  0  0  0  0  0  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  0  8  8  8  8  8  8  0  8  0  0  8  8  8  0  0  0  0  8  0  8  0  0  8  0  8  8  8  8
 0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  0  0  8  8  0  0  8  8  0  0  8  8  8  0  8  8  0  0  0  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+57x^36+4x^38+120x^40+60x^42+221x^44+512x^45+2180x^46+512x^47+204x^48+52x^50+100x^52+8x^54+41x^56+21x^60+1x^64+1x^68+1x^72

The gray image is a code over GF(2) with n=368, k=12 and d=144.
This code was found by Heurico 1.16 in 0.379 seconds.