The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  4  4  4  4  4  2  4  1  2  4  4  4  1
 0 12  0  0  0  0  0  0  0  0  0  8  4  4  4  8 12  0  4  4 12  8  8  0 12  0 12  0  4 12  4 12  4  4  0  4 12  8  4  8 12  8 12  4  8 12  8  4
 0  0 12  0  0  0  0  0  0  0  0 12  8 12  4  4 12 12 12  0  8  8  0  8  8 12 12 12 12  4  0  4  8  4  8 12  0 12  8  8 12  8 12  8  4  4 12  0
 0  0  0 12  0  0  0  4 12 12  8  4 12  0 12  4  8 12  8 12  8  0 12 12  0  8  0  4 12 12  0 12 12  4 12  8  8  8  0  8  8  8  0  4  4  0  4  0
 0  0  0  0 12  0  4  4  4  0  8  0  0  0  0  0  0 12  4 12  8 12  4  8  4  8  8  8 12  0  4  4  4  0  8  8 12 12  4  0  0  4  0  8 12  8  0  4
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  0  4  4 12  4  0 12  8  0  0 12 12 12  8  8  8  8  0 12  4  4  8  4  0  8  4 12  0  0  4  8  4  8  0
 0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  8  8  0  0  8  0  8  0  8  0  8  0  0  8  8  8  0  0  8  0  0  0  0  0  8  0  8  0  0  8  0  0  8

generates a code of length 48 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+157x^38+455x^40+20x^41+937x^42+384x^43+1943x^44+1896x^45+3711x^46+3856x^47+6031x^48+3840x^49+3878x^50+1888x^51+1898x^52+376x^53+847x^54+16x^55+374x^56+12x^57+185x^58+47x^60+13x^62+2x^64+1x^72

The gray image is a code over GF(2) with n=384, k=15 and d=152.
This code was found by Heurico 1.16 in 18.5 seconds.