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

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

Homogenous weight enumerator: w(x)=1x^0+180x^40+24x^41+302x^42+96x^43+780x^44+416x^45+1440x^46+1440x^47+2481x^48+2192x^49+2360x^50+1440x^51+1547x^52+416x^53+636x^54+96x^55+298x^56+24x^57+122x^58+70x^60+4x^62+16x^64+3x^68

The gray image is a code over GF(2) with n=392, k=14 and d=160.
This code was found by Heurico 1.16 in 13.9 seconds.