The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 12  0  4  0  0  4 12  0  0  4 12  8 12  8  4  8  4  0  0 12  8 12  8  4  8 12  8  4  8  8 12  4  0  8  4  4  8  0
 0  0 12  4  0 12  4  0  8  4 12  8  8 12  4  0  4 12  8  4  8  8  4  4  8  0 12 12  0  0 12  4  8  0  4  4  4  0  0
 0  0  0  8  8  8  0  8  8  8  8  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+22x^36+72x^38+320x^39+77x^40+16x^42+3x^44+1x^76

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 0.0336 seconds.