The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+40x^40+64x^41+77x^42+326x^43+590x^44+1226x^45+1973x^46+2478x^47+2868x^48+2482x^49+1966x^50+1234x^51+558x^52+318x^53+60x^54+58x^55+26x^56+6x^57+11x^58+12x^60+7x^62+1x^64+2x^66

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 2.36 seconds.