The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  1  1  1  1  1  2 12  1  1  1  2  1  1  1  1  1  1  0  2  0  4  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  6  2  4  0 10  6  8  6  0 10  2  0 14  6  6 10 10 10 14  2  0  2  6  2  8  0  0
 0  0  8  0  0  0  0  0  0  0  8  0  8  8  0  8  0  8  8  8  0  0  8  8  8  8  8  8  8  0  0  0  0  0  0  8  8  0  0
 0  0  0  8  0  0  0  8  0  0  8  0  8  8  8  0  8  0  0  0  8  8  8  8  8  8  0  0  0  0  8  0  0  8  8  0  0  0  0
 0  0  0  0  8  0  0  8  8  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  0  8  0  8  8  8  0  0  8  0  8  0  0  0
 0  0  0  0  0  8  0  8  0  0  0  8  8  0  0  8  0  8  8  0  8  8  0  8  8  8  0  8  8  8  0  8  8  8  8  8  8  8  0
 0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  0  0  8  0  0  0  8  8  0  8  0  8  0  8  0  0  8  0  8  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+41x^32+179x^34+426x^36+1437x^38+1338x^40+470x^42+163x^44+18x^46+12x^48+7x^50+2x^52+1x^54+1x^60

The gray image is a code over GF(2) with n=312, k=12 and d=128.
This code was found by Heurico 1.16 in 0.214 seconds.