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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+56x^32+110x^36+96x^38+1536x^39+126x^40+32x^42+58x^44+25x^48+7x^52+1x^68

The gray image is a code over GF(2) with n=312, k=11 and d=128.
This code was found by Heurico 1.16 in 0.0911 seconds.