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

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

Homogenous weight enumerator: w(x)=1x^0+64x^30+109x^32+101x^34+163x^36+512x^37+2233x^38+512x^39+145x^40+102x^42+58x^44+54x^46+32x^48+5x^50+3x^52+1x^54+1x^56

The gray image is a code over GF(2) with n=304, k=12 and d=120.
This code was found by Heurico 1.16 in 41.2 seconds.