The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  8  2  1  1  1  2  1  1  0  2  2  1  1  1  2  1  1  1  1  1  2  1  4  1  2  2  2  1  2  1
 0  2  0  6  4  6 12  2  8  6 12 14  0  2  4 14  6  6  2  2 14  4 10  0  6  8  2  2 10 14  2  0 14  2 10  2  0 12  2 14  0  4 12  8  4 14 14  6  2
 0  0 12  0  4  0  0  0  8  4  4  4  4 12  8  0  4  8 12  8 12  0  4  8 12  8  0  0  0  0  0  0  0  4  4  8  4  4  8  4  4 12  4  4  0  4  4 12  0
 0  0  0 12  0  0  0  4 12  4 12  8 12  8 12 12  4  0 12 12  8  0 12  8  4  4  8  0  0  4  8  0  4  8  4  4  0  0  4  0  8  0  4 12  4  8  0 12  4
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  8  8  0  0  8  0  0  0  0  8  0  0  8  0  8  8  8  8  0  0  8  8  0  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  0  8  8  8  0  0  0  8  8  8  8  8  0  8  0  8  8  0  8  8  0  0  0  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  0  8  8  0  8  8  0  8  8  8  8  8  0  0  8  0  8  0  0  0  8  0  8  0  8  0  8  8  8  0  8  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  8  8  8  8  8  0  0  0  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+162x^40+56x^41+416x^42+412x^43+839x^44+1364x^45+2074x^46+3340x^47+4789x^48+5940x^49+4594x^50+3540x^51+2172x^52+1276x^53+726x^54+388x^55+422x^56+68x^57+118x^58+49x^60+8x^62+10x^64+4x^68

The gray image is a code over GF(2) with n=392, k=15 and d=160.
This code was found by Heurico 1.16 in 15.3 seconds.