The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1  1 10  1  1 12  1  0  1 12  1  1  1  1  1
 0  1  3  6  5  1 12 15  1 10  9  1  0  3  1  6  5  1 12 15 10  1  0  9  1  9  1  5  1  3  5 12  3  9
 0  0  8  0  0  0  0  8  0  8  8  8  0  0  0  8  8  8  0  0  0  0  0  8  0  8  8  0  0  8  8  8  0  8
 0  0  0  8  0  0  8  8  0  8  0  8  0  8  8  8  0  0  8  0  8  8  8  8  0  0  0  0  0  0  8  0  0  8
 0  0  0  0  8  0  8  0  8  8  8  8  0  8  0  0  8  0  0  8  8  0  0  8  0  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  0  8  0  0  0  0  8  8  8  8  0  0  8  0  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+182x^30+128x^31+773x^32+384x^33+1184x^34+384x^35+752x^36+128x^37+164x^38+8x^40+6x^46+2x^48

The gray image is a code over GF(2) with n=272, k=12 and d=120.
This code was found by Heurico 1.16 in 1.67 seconds.