The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1  1  1 10  1  1  0  1 12  1  1  6  1  1  1  0  0  0  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 15 12 10  1  9  0  1  6  1  3  5  1 15  3  0  1  1  1  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  0  0  8  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  8  0  8  0  8  8  8  0  0  8  0  8  0  0  0  8  8  8  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  8  8  0  0  0  0  0  0  8  8  0  8  0  8  0  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  8  0  0  0  8  0  8  0  0  8  8  8  0  0  8  8  0  8  0  8  0  0  8
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  0  8  0  0  8  0  8  0  8  0  0  8  8  8  0  8  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  8  8  0  8  8  0  0  8  0  8  0  0  8  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  0  0  8  0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  8  8

generates a code of length 39 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+40x^30+16x^31+114x^32+176x^33+331x^34+768x^35+2221x^36+3920x^37+5491x^38+6624x^39+5502x^40+3920x^41+2226x^42+768x^43+310x^44+176x^45+82x^46+16x^47+31x^48+19x^50+13x^52+3x^54

The gray image is a code over GF(2) with n=312, k=15 and d=120.
This code was found by Heurico 1.16 in 6.39 seconds.