The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+107x^36+32x^38+425x^40+420x^42+1672x^44+3512x^46+2048x^47+6230x^48+4096x^49+5816x^50+2048x^51+3886x^52+1344x^54+747x^56+132x^58+184x^60+8x^62+52x^64+7x^68+1x^80

The gray image is a code over GF(2) with n=392, k=15 and d=144.
This code was found by Heurico 1.16 in 18.6 seconds.