The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+72x^29+173x^30+362x^31+463x^32+616x^33+823x^34+632x^35+420x^36+250x^37+123x^38+82x^39+24x^40+20x^41+17x^42+12x^43+4x^44+2x^45

The gray image is a code over GF(2) with n=272, k=12 and d=116.
This code was found by Heurico 1.16 in 0.28 seconds.