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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+28x^34+94x^36+64x^37+152x^38+384x^39+126x^40+64x^41+60x^42+34x^44+16x^46+1x^64

The gray image is a code over GF(2) with n=312, k=10 and d=136.
This code was found by Heurico 1.16 in 0.369 seconds.