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

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

Homogenous weight enumerator: w(x)=1x^0+105x^36+48x^37+24x^38+672x^39+66x^40+48x^41+8x^42+51x^44+1x^72

The gray image is a code over GF(2) with n=312, k=10 and d=144.
This code was found by Heurico 1.16 in 16 seconds.