The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  1  8  2  0  1  1  8  1  1 12  1  1  1  4  1  2  2  1
 0  2  0  6  0  6  8  6  6  0 14  4 14  4  4  2  4  6  2  6 14  2 14  2 12  2  2  6  4  2  2  4  6  8  2 14  6  0
 0  0 12  0  0  0 12  0  4  0 12  4  4  4  8  0  8 12  8  4 12  4  4 12  8  4  8 12  0  4  0  0  0  4  8  4  0  0
 0  0  0 12  0  0  0  4  4  4 12  4  8  0  0  8 12  4  4  0  0 12  4  8 12  4  4  8  8  4  0  8 12  0  8  8  8  0
 0  0  0  0 12  0  4  4  8 12 12 12  0  0  8 12  0  8  4  4 12 12 12 12  8  0  8  8 12  8  4  8 12  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  0  0  8  0  0  8  0  8  8  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+48x^30+80x^31+173x^32+360x^33+604x^34+1126x^35+1809x^36+2530x^37+2982x^38+2558x^39+1757x^40+1130x^41+597x^42+306x^43+131x^44+70x^45+53x^46+26x^47+33x^48+6x^49+3x^50+1x^54

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 2.81 seconds.