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

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

Homogenous weight enumerator: w(x)=1x^0+220x^30+540x^32+886x^34+1178x^36+3306x^38+20480x^39+3340x^40+1174x^42+901x^44+530x^46+183x^48+28x^50+1x^76

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 13.5 seconds.