The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  1  2  2  1  1 12  2  1  2  1  1  0  1  2  2  1  2
 0  2  0  2  8  0  6 14  0  8  6  2  0 10  0  2  2 12  4 12  4  6 12  2 14  6  2  4  8  8 10 14  2  4  0
 0  0  2  2  0 14  6  8  4 10  2  8  4 14 14 12  4  2 14 14 14  6 12 10  0  8  2  8  6  2  8  4 10 10  2
 0  0  0  4  4  4  0  4 12  4  8  4  0  4  8  8  4  8 12 12  0  4  4 12  4  0  0  0  0  8  8  0  4  8 12

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

Homogenous weight enumerator: w(x)=1x^0+218x^31+373x^32+486x^33+679x^34+714x^35+686x^36+410x^37+224x^38+162x^39+72x^40+46x^41+8x^42+10x^43+2x^44+2x^45+2x^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 10.4 seconds.