The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+52x^29+99x^30+162x^31+200x^32+392x^33+747x^34+868x^35+716x^36+394x^37+190x^38+106x^39+62x^40+44x^41+17x^42+16x^43+12x^44+14x^45+2x^46+1x^48+1x^54

The gray image is a code over GF(2) with n=280, k=12 and d=116.
This code was found by Heurico 1.16 in 0.27 seconds.