The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12  1  1 10  1  0  1  1  1  1  6  1  1  1 12  1  1  1 12 10  1  0  1  1  1  1  1  1  2  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5  1 12 15  1 10  1  9  6  5  0  1 10  3 12  1  9  5  6  1  1 12  1 12  0  5 10 12  3  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  8  8  8  8  0  8  0  8  8  0  0  0  0  8  8  0  0  8  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  8  8  8  0  0  0  8  0  0  8  8  0  8  0  0  0  8  0  8  8  0  0  0  0  0  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  0  0  8  8  8  0  8  0  0  8  8  8  0  0  0  8  8  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  8  8  0  8  8  8  0  0  0  8  0  8  8  0  8  8  8  8  0  0  8  0  0  8  0  8  0  0  8  8  8  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  8  0  8  8  8  8  0  8  0  8  8  8  0  8  8  8  8  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  8  0  8  0  8  8  8  0  8  8  0  0  0  8  0  0  0  8  8  0  0  8  8  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+21x^40+146x^42+40x^43+401x^44+560x^45+1188x^46+2008x^47+2346x^48+2976x^49+2356x^50+2008x^51+1202x^52+560x^53+371x^54+40x^55+108x^56+24x^58+11x^60+8x^62+3x^64+2x^66+2x^68+1x^70+1x^72

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 2.38 seconds.