The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+105x^40+8x^41+156x^42+80x^43+601x^44+384x^45+1448x^46+1456x^47+2856x^48+2288x^49+2736x^50+1456x^51+1542x^52+384x^53+504x^54+80x^55+209x^56+8x^57+20x^58+45x^60+13x^64+4x^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 4.29 seconds.