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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+263x^40+112x^42+256x^43+488x^44+768x^45+288x^46+768x^47+582x^48+256x^49+112x^50+152x^52+48x^56+1x^64+1x^72

The gray image is a code over GF(2) with n=368, k=12 and d=160.
This code was found by Heurico 1.16 in 67.7 seconds.