The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+26x^39+113x^40+122x^41+227x^42+300x^43+688x^44+1408x^45+960x^46+3284x^47+1808x^48+3236x^49+1695x^50+1400x^51+400x^52+336x^53+128x^54+98x^55+54x^56+18x^57+57x^58+12x^59+7x^64+5x^66+1x^72

The gray image is a code over GF(2) with n=384, k=14 and d=156.
This code was found by Heurico 1.16 in 83.5 seconds.