The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+18x^38+16x^39+9x^40+16x^41+2x^42+2x^44

The gray image is a code over GF(2) with n=312, k=6 and d=152.
This code was found by Heurico 1.16 in 0.0211 seconds.