The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2  1 12  1  2  0  1  1  1  2  1 12  2  1  1  1  1  1  1  2  1  2  1
 0  2 12  6  0  6 12 10  0  6 12 10  6  2  0  6 10 10  2 12  6  2  0 12  0 10  6  2  6  0 10 12 12  4 10 12 12 12  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  8  0  0  8  0  8  0  0  8  8  8  8  8  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  0  0  0  0  8  0  0  8  8  8  8  0  0  0  8  0  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  8  0  8  0  0  0  8  0  8  0  0  8  0  0  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  0  8  0  8  0  0  0  8  8  8  8  8  8  0  8  0  0  8  8  0  0  8  0  0  0  8  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  8  0  0  8  8  8  8  8  8  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  8  0  0  0  0  8  8  0  0  0  0  8  8  8  8  8  0  8  0  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  0  0  8  8  0  0  8  8  8  8  0  8  8  0  8  8  0  0  0  0  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+44x^30+8x^31+176x^32+64x^33+347x^34+288x^35+1090x^36+2240x^37+1925x^38+4016x^39+1956x^40+2240x^41+1106x^42+288x^43+309x^44+64x^45+138x^46+8x^47+41x^48+19x^50+8x^52+5x^54+2x^56+1x^60

The gray image is a code over GF(2) with n=312, k=14 and d=120.
This code was found by Heurico 1.16 in 2.84 seconds.