The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+146x^36+48x^38+506x^40+32x^41+400x^42+352x^43+1145x^44+2336x^45+3136x^46+5472x^47+5619x^48+5472x^49+3136x^50+2336x^51+1182x^52+352x^53+400x^54+32x^55+469x^56+48x^58+114x^60+28x^64+4x^68+1x^72+1x^76

The gray image is a code over GF(2) with n=384, k=15 and d=144.
This code was found by Heurico 1.16 in 42 seconds.