The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^36+8x^37+38x^38+8x^39+266x^40+200x^41+430x^42+328x^43+1942x^44+688x^45+6444x^46+816x^47+10290x^48+816x^49+6444x^50+688x^51+1924x^52+328x^53+430x^54+200x^55+240x^56+8x^57+38x^58+8x^59+78x^60+17x^64+4x^68+2x^72

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 13.5 seconds.