The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+240x^30+254x^32+1008x^34+1024x^35+1088x^36+272x^38+192x^40+16x^42+1x^64

The gray image is a code over GF(2) with n=280, k=12 and d=120.
This code was found by Heurico 1.16 in 0.321 seconds.