The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  1  1  1  1  1  2  1  1  1  2  1  1  1  1  2  2  4  4  4
 0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  0  8  8  0  8  8  8  8  0  0  0  8  8  8  8  0  0  8  8
 0  0  8  0  0  0  0  0  0  0  8  0  8  0  8  0  8  8  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  0  0  0  0  0  0
 0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  0  0  0  8  8  8  0  0  8  0  0  8  0  8  8  0  8  8  0  0  0  0  8  0
 0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  8  8  8  0  8  8  0  8  8  0  0  8  0  8
 0  0  0  0  0  8  8  0  8  8  0  0  8  8  8  8  8  0  0  8  8  0  8  0  8  0  0  0  8  0  0  8  8  0  8  8  0  8  8

generates a code of length 39 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+74x^36+48x^38+256x^39+89x^40+16x^42+22x^44+5x^48+1x^56

The gray image is a code over GF(2) with n=312, k=9 and d=144.
This code was found by Heurico 1.16 in 0.154 seconds.