The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+92x^40+112x^42+382x^44+804x^46+512x^47+1735x^48+1024x^49+1604x^50+512x^51+906x^52+268x^54+155x^56+28x^58+38x^60+16x^64+2x^68+1x^72

The gray image is a code over GF(2) with n=392, k=13 and d=160.
This code was found by Heurico 1.16 in 1.49 seconds.