The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+256x^30+392x^32+804x^34+360x^36+188x^38+14x^40+28x^42+4x^46+1x^48

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 53.9 seconds.