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  2  1  1  4  4  4  4  2  2  2  2  1  4
 0 12  0  0  0  0  0  0  0  0  8 12 12  4  8 12  0  4 12  8 12  8  0 12  4  8  4  4 12 12  8  0 12  8  0  4  0  8
 0  0 12  0  0  0  0  0  0  0 12 12  4  8  4  4 12  0 12  0  0  8  8  8  8  4 12  4  8  0  8  4 12  0 12 12  4  8
 0  0  0 12  0  0  8 12 12  4  4  8  4  4 12  8  0  4 12  0  0  4  4  0  8  0 12  8  0 12  8  4  4 12  0  8  0  4
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  8  4  4  4  4  8  0  4  0  4  4  8  8  4 12  0  4  4  4 12  8  4 12  4
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  4  8  4  0 12  0 12  4  8  0 12  8  4  8 12  4  8  4 12  0  4  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+168x^30+432x^32+52x^33+772x^34+736x^35+2003x^36+2364x^37+3500x^38+2176x^39+2040x^40+716x^41+754x^42+96x^43+365x^44+4x^45+144x^46+54x^48+6x^50+1x^56

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 3.64 seconds.