The generator matrix

 1  0  1  1  1 14  1  1  8  1  1  6  1  1 14 12  1  1  1 10  8  1  1  1  1  1  1  1 10  1  1  1  1  8  1
 0  1 11  6  5  1 13  0  1  2  3  1 14 11  1  1  9  1  6  1  1 15  0 14  5  6 12  4  1  6  2  5  8  1  5
 0  0 12  0  0  8  0 12 12  4  4  4 12  8  4  4 12  4  4  8  8  0  8  0  4 12  4  4 12  8  4 12  0 12 12
 0  0  0 12  8 12  4 12  8  0  4 12  8 12  8  4  4  0 12  8 12  0  0  4  4  4 12  0  8  0  8  0 12 12 12

generates a code of length 35 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+94x^31+348x^32+554x^33+815x^34+516x^35+814x^36+532x^37+300x^38+86x^39+14x^40+2x^41+4x^42+8x^43+6x^44+1x^48+1x^50

The gray image is a code over GF(2) with n=280, k=12 and d=124.
This code was found by Heurico 1.16 in 0.148 seconds.