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  2  2  1  1  1  1  2  2  1  1  2  1  1  1  1  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  0  8  8  8  0  0  0  8  8  8  8  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  8  0  0  8  8  8  8  8  8  0  0  8  8  8  0  0  8  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  0  0  0  8  8  0  8  0  0  8  8  8  8  0  8  0  8  8  0  8  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  8  8  0  8  8  8  0  0  0  8  8  0  0  8  8  0  0  8  8  0  8  8  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  8  8  8  0  8  0  0  0  0  8  0  8  0  8  0  8  8  0  8  8  0  8  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  8  0  8  8  0  8  0  8  0  8  0  0  8  0  0  0  8  8  8  8  8  8  8  8  0  8  0  8  8  8
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  0  8  0  0  0  8  8  8  0  0  0  8  8  0  8  0  8  8  0  0  8  8  0  8  0  0  8  8  0  8  8
 0  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  0  0  8  0  8  0  0  8  0  0  0  0  8  8  8  0  8  8  8  8  8  8  0  8  8  8  8  8  8  0  8  8  8
 0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  0  0  0  8  0  0  8  8  0  0  8  0  8  8  0  8  0  0  0  0  0  8  0  8  8  8  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  8  8  8  8  8  0  8  0  8  0  0  0  0  0  0  0  0  0  0  8  8  0  8  8  0  0  8  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+110x^36+263x^40+422x^44+320x^46+1023x^48+12288x^49+640x^50+736x^52+64x^54+296x^56+166x^60+48x^64+6x^68+1x^88

The gray image is a code over GF(2) with n=392, k=14 and d=144.
This code was found by Heurico 1.16 in 5.6 seconds.