The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+74x^34+8x^35+164x^36+64x^37+180x^38+1136x^39+161x^40+64x^41+95x^42+8x^43+40x^44+34x^46+15x^48+1x^50+2x^52+1x^64

The gray image is a code over GF(2) with n=312, k=11 and d=136.
This code was found by Heurico 1.16 in 0.0914 seconds.