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  2  2  2  2  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  8  0  8  0  8  8  0  8  8  0  8  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  0  8  8  8  0  8  8  8  8  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  8  0  8  0  0  0  8  0  8  8  8  8  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  0  0  0  8  8  0  8  8  8  8  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  8  8  8  0  0  8  8  0  0  8  0  0  0
 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  0  8  8  8  8  0  8  0  0  0  0  0  0
 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  0  8  8  0  8  8  8  8  0  0  0  0
 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  8  8  8  0  8  0  8  0  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  8  0  0  8  0  0  0  0  8  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  8  8  8  0  0  8  0  8  0  8  0  0

generates a code of length 44 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+130x^32+317x^36+32x^38+556x^40+480x^42+13342x^44+480x^46+600x^48+32x^50+279x^52+116x^56+13x^60+5x^64+1x^76

The gray image is a code over GF(2) with n=352, k=14 and d=128.
This code was found by Heurico 1.16 in 4.77 seconds.