The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+53x^30+56x^31+105x^32+64x^33+234x^34+1048x^35+238x^36+64x^37+86x^38+40x^39+34x^40+6x^42+8x^43+2x^44+4x^46+4x^48+1x^62

The gray image is a code over GF(2) with n=280, k=11 and d=120.
This code was found by Heurico 1.16 in 94.1 seconds.