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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+167x^30+419x^32+8x^33+624x^34+360x^35+1840x^36+2704x^37+4152x^38+2704x^39+1848x^40+360x^41+650x^42+8x^43+334x^44+161x^46+35x^48+6x^50+2x^52+1x^64

The gray image is a code over GF(2) with n=304, k=14 and d=120.
This code was found by Heurico 1.16 in 3.63 seconds.