The generator matrix

 1  0  1  1  1 14  1  2  1 12  1  1  1  1  8  1  1  0  1  1  1  1  4  0  6  6 10 10  2  0 12  1  1  2  1  1
 0  1 11  6 13  1 12  1  7  1 14  5  8  3  1  2  9  1  4 15 10  1  1  1  1  1  1  1  4  1  1  3  9 10 12  6
 0  0 12  0  4  4  8  4  4  8  4  0 12  8 12  4  0  0 12  8  8 12 12  8  0  0  0  8  4 12  4  0  0  4  8  0
 0  0  0  8  0  8  8  8  8  0  0  8  0  8  0  8  0  8  8  0  0  8  0  8  0  0  8  8  0  8  8  0  8  0  0  8
 0  0  0  0  8  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  0  0  8  0  8  8  8  8  8  8  8  0  8  8  8

generates a code of length 36 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+163x^32+288x^33+532x^34+736x^35+758x^36+736x^37+376x^38+288x^39+186x^40+20x^42+2x^44+10x^48

The gray image is a code over GF(2) with n=288, k=12 and d=128.
This code was found by Heurico 1.16 in 0.185 seconds.