The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2 12  2  8  2  4  2  2  2  2  1  1  1  1  1  1  1  1  4  0  1
 0  2 12  6  8 14  4 10  0  6 12 10  8 14  6  2  4  2 10  2 14  2  2  2  0 12  8  4  0 12  8  4  6 10 14  2 12  4  0

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

Homogenous weight enumerator: w(x)=1x^0+36x^38+40x^39+39x^40+8x^41+3x^42+1x^50

The gray image is a code over GF(2) with n=312, k=7 and d=152.
This code was found by Heurico 1.16 in 0.0181 seconds.