The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^39+148x^40+268x^41+509x^42+772x^43+1272x^44+2180x^45+3625x^46+4836x^47+5335x^48+4940x^49+3608x^50+2212x^51+1279x^52+724x^53+392x^54+252x^55+140x^56+72x^57+51x^58+24x^59+16x^60+8x^61+7x^62+1x^68

The gray image is a code over GF(2) with n=384, k=15 and d=156.
This code was found by Heurico 1.16 in 14.9 seconds.