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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+192x^30+126x^32+1408x^34+128x^36+192x^38+1x^64

The gray image is a code over GF(2) with n=272, k=11 and d=120.
This code was found by Heurico 1.16 in 0.096 seconds.