The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^38+96x^39+13x^40+2x^42+2x^44+1x^46+1x^54

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 0.0286 seconds.