The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+77x^42+175x^44+16x^45+338x^46+128x^47+1221x^48+224x^49+1233x^50+128x^51+323x^52+16x^53+106x^54+56x^56+33x^58+13x^60+4x^62+2x^64+1x^66+1x^84

The gray image is a code over GF(2) with n=392, k=12 and d=168.
This code was found by Heurico 1.16 in 0.451 seconds.