The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  0  1  1  1  6  1  1  1 10  1  1  1 12  0  1  6  1  1  1  1  1  0  0  1  1  1
 0  1  3  6  5  1 12 15  1 10  9  1  0  1  3  6  5  1 12  9 10  1  0  9 15  1  1  3  1  6  5  5 12 12  2  2  5  3  0
 0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  0  8  8  8  8  0  8  0  0  8  0  8  8  8  8  8  8  8  0  8  8  8  0  0
 0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0  0  0  0  8  8  8  8  8  0  0  8  8  8  0  8  0  8  0  0  0
 0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  8  0  0  8  8  0  0  0  0  8  0  8  0  8  0  8  8  8  0  8  0
 0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  0  8  0  8  8  0  0  0  8  8  0  8  0  8  8  8  8  8  8  8  0  0  0
 0  0  0  0  0  0  8  8  0  8  0  8  8  8  8  8  8  8  8  0  8  0  0  0  8  0  8  0  0  0  0  8  8  8  8  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+23x^32+40x^33+109x^34+302x^35+521x^36+1112x^37+1135x^38+1702x^39+1162x^40+1112x^41+519x^42+298x^43+77x^44+40x^45+22x^46+2x^47+6x^48+3x^50+1x^52+3x^54+1x^58+1x^60

The gray image is a code over GF(2) with n=312, k=13 and d=128.
This code was found by Heurico 1.16 in 0.442 seconds.