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

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

Homogenous weight enumerator: w(x)=1x^0+139x^36+48x^37+248x^38+160x^39+290x^40+48x^41+40x^42+44x^44+5x^48+1x^68

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 57.6 seconds.