The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+151x^40+24x^41+332x^42+168x^43+985x^44+888x^45+2174x^46+1992x^47+3070x^48+1992x^49+2118x^50+888x^51+890x^52+168x^53+330x^54+24x^55+121x^56+38x^58+19x^60+9x^64+2x^68

The gray image is a code over GF(2) with n=384, k=14 and d=160.
This code was found by Heurico 1.16 in 4.05 seconds.